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Good points. 
It’s true that one person’s biopsy could be used in one experiment and another person’s biopsy used in many experiments. However the person that produced the biopsy doesn’t influence whether the biopsy is useful or not. It is just luck. It was lock that Henrietta Lack’s biopsy was so successful. I would rather have everyone get modest compensation rather than one person get a giant windfall due to luck. Having one person earn a windfall makes it seem like a lottery. We as a society have decided not to give people compensation for their biopsies in order to discourage people getting unnecessary biopsies for money. That makes a lot of sense to me. Therefore the current system seems reasonable.
I think her contribution should be acknowledged, but that’s different than saying celebrated. When you celebrate someone, you applaud their actions. She didn’t actually do anything. There’s nothing to say that she’s a particularly good or bad person. She’s just a person. I think telling her story and acknowledging her as reasonable, but to celebrate her doesn’t make sense to me since she didn’t do anything to celebrate.  
As for giving her relatives some goodwill compensation, I agree with that and that is already been done. However they keep asking and actually demanding more. It would be nice if we could just settle this, but they take a pay out and then keep complaining that they deserve more. That seems unseemly.
and the practice of using patient biopsy tissue for research was relatively routine. 

Do you have any information regarding legal patient consent requriements in this matter? As far as I know, all of this happened without Lacks' consent.
EDIT: clarified legal requriements >

That was the controversy. I read the book on her and the it all happened without her consent nor knowledge. It seems valid to want compensation for that >

At the time, no one was getting consent. Shouldn’t everyone be compensated? Isn’t better medicine a compensation itself? >

But I think, or at least hope, we can all acknowledge that that was a bad practice. Does the fact that an organization wronged someone within the confines of the law necessitate that they should never have to make amends? The topic of reparations today is a controversial one, but I think if we simplified it by looking at immediately after slavery was abolished, I think most people would agree to a system where the slave owners paid reparations for their ill gotten gains under slavery. Granted, we are about one human lifetime out from Henrietta's death, but it is still a shorter period of time than slavery and her descendents could undeniably have benefited from her being fairly compensated. The Constitution specifies you can't go to jail for an act that became illegal after you did it, but you need not break the law to owe damages in civil court. >

I think the opposition here is, where do we draw the line? If you just open the floodgates for descendants of people who didn't consent to testing before 'x' date, it'll be a madhouse of people clamoring for their reparations money. Whereas if we don't set that precedent, some (dead) people won't get compensation, but neither does anyone else, whose claim may or may not be legitimate. And then we can put the whole thing behind us and move forward together, having learned from our ancestor's mistakes. >

To me, this argument boils down to "so much wealth was stolen by medical researchers, how could you possibly expect them to pay it back?" I get acknowledging historical context is important, but this was the 1950s, we knew that samples for medical testing had monetary value, and we knew that taking something of value from someone without permission, or even compensation is wrong. This isn't a case of collective morals not being as evolved as they are today, or of society not having the perspective to see the wrong in this situation, it is a case of businesspeople exploiting a new and unregulated commodity. >


so much wealth was stolen by medical researchers, how could you possibly expect them to pay it back?

But like... yes?
I mean if it's simply not possible for it all to be paid back, then it can't be paid back can it? 
What are we going to do? Shut down all future medical research and divert that money into the decendants of those unethically researched on? Clearly this would be a worse outcome for society.
Or just pay off the loudest voices by diverting some of the money for future medical research? Again this isn't great for society, and is inequitable in that those who can afford a loud voice get the money.
There's little value in paying off the decendants. They've no financially worse off for the previous research, it's not like they can show a financial loss. The ownership of the material at the time wasn't established as belonging to her estate either. 
From a utilitarian perspective this is a total non-starter in terms of ethics. >

We are talking about companies who sell life saving medication because of this research, and to some extent probably also the US government. The thing that really bothers me about their claim is they did work on producing marketable treatments, so descendents clearly aren't entitled to all of the money from that treatment, so they have by necessity made an amount of money proportional to the value of the research sample. A court could just say 'Foe X number of years this estate gets Y percent of the profits from all products derived from the research sample provided.They have enough money to pay a meaningful sum to everyone effected, if not the true value of their contribution.
Of course the descendents have seen a financial loss. A company stole the most valuable thing Henrietta owned at a time when she was paying huge medical bills. She probably didn't have any assets to leave to her family when she passed. Had she been fairly compensated, they would. >

I do understand the angle, however they didn't actually steal it. Stealing means taking something illegally.
Taking biopsies and examining them to try and help diagnose and treat cancer is absolutely common practice and happens all the time. There were issues of specific consent for the procedure done to the patient, however getting consent like this wasn't commonly done in those days like it is now and taking the biopsy followed the law and the customs of the time. For sure that wouldn't have passed muster today, but times change and you can't retrospectively punish people for new laws.
Once the biopsy was examined, it became medical waste. Now I'm pretty sure you don't have any consent involved as to the end use of what you flush down the toilet every day, that's your waste but it ceases to be your property once it's flushed. This is very much the same deal, it was considered waste and therefore no longer the property of the patient. Again in current times if research was to be done on your medical waste you'd be asked to consent, but that wasn't the case then. In current times sewage solids are sold and often used as fertiliser, by analogy you'd be claiming part of the profit of all the tomatos sold just because there was some of your poop in there originally.
Finally what was done was de jure not illegal, it was challenged in court, and the court decided in their outcome that this wasn't theft because there was no loss of property (as it was waste). Therefore it's been specifically decided this wasn't stealing.
Now don't get me wrong here, I think there are some ethical issues involved in this case, and fortunately these have all been thrashed out in modern medical research. However there's really little grounds in this case to claim that the decendants of the patient can claim some of the profits because there's been some profit made from using waste material. >


My perspective is that Henrietta Lacks didn’t do anything to further the research, at least not more than anyone else who has ever had their tissue used in research. The only difference is that her tissue happens to proliferate.

Well that seems to be a pretty big difference, wouldn't you agree? One persons biopsy may get used in one experiment. HeLa cells have been used in millions of experiments, including in the development of modern drugs which have produced billions in revenue.
Now I'm not saying her relatives are obligated to financial compensation, but given the significance of her contribution to the world, I thought we would've given them some good will money by this point.
Sure, Henrietta didn't do anything special to have these unique cells. But that doesn't mean she shouldn't ever be celebrated or rewarded for it.