For a while, he had access to the Dharma stores of food.
The timeline on the show was slower than our real-life timeline, so it seemed like they were on the island for much longer than they actually were.
Also, he did lose weight:
"I'm down a notch in my belt.
I'm a big guy.
It's gonna be a while before you want to give me a piggy back ride".
(Episode "Confidence Man")
Out of Universe:
That's the part of Lost that raises the most questions for you? :)
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@Johnny
Bones is totally correct and provides the correct in-universe answer.
I just wanted to add a rather boring out of universe answer to say that the obvious reason is that Jorge Garcia , the actor who played Hurley, simply didn't lose much weight.
So whilst we can search for plenty of realistic in-universe reasons to justify this, the fact is he's a big guy with a serious obesity problem .
There are plenty of claims online that he was asked not to lose weight by the producers, as his character was so popular "as is"
(and it gave joke-content on screen e.g. Sawyer mocking Hurley) -
but I can't find any evidence this was the case.
Note:
He does lose some weight after Season 1, just not much :
"I can afford to not live on rum and burritos and take better care of myself...
Besides, there were enough people who were waiting for my character to lose weight as a result of being stranded on a desert island."
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Weight loss (or gain) is not always due to diet.
If it were, every diet would work.
Sometimes it's due to Hypothyroidism, which is an underactive thyroid gland.
If you have this, it's nearly impossible to combat weight gain without medical help.
Of course, Hugo wasn't jogging an hour a day, and there's no telling how many Dharma Cookies he was eating off-screen, so it's possible that once food stores were found he could actually gain weight if he had this condition.
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I think any medical condition speculation is pointless to even mention.
While hypothyroidism may make it easier to gain weight, your body still obeys the laws of thermodynamics.
Simply put, Hurley was not eating at a large enough deficit to show noticeable weight loss.
It's been years since I watched Lost, but I can't remember any of the characters showing noticeable changes in weight.
From that it's easy to conclude that there was sufficient food supply for all of the characters to roughly maintain their weight since the start of the show.
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SPOILERS INTERLEAVED
There are a few scenes specifically in the show where we see Hugo overindulging on-island.
He was also in charge of food distribution whenever it came up in the show and from his flashbacks we know he has issues with food consumption.
From this we could deduce that he might get the bigger cut of food for distributing it to everyone or he might take a secret cut because he has the opportunity to (the latter which is brought up on the show with his food cache).
[ http://lostpedia.wikia.com/wiki/Hugo_%22Hurley%22_Reyes (CTRL+F food)]
The total amount of on-island time is very deceiving with the flashbacks and whatnot interleaved with the story.
The total amount of time spent on the island after the crash was only ~108 consecutive days.
3 months is not a lot of time for drastic weight change when you factor in Hurley's overindulging and food caches, plus he was already from a hot climate before crashing on the island
so sweating off the weight doesn't seem plausible.
[ http://lostpedia.wikia.com/wiki/Timeline ] Finally there is the healing/spiritual aspect of the island.
It was never outright stated that healing means to return to the optimal human form.
But rather is feels more like physical healing combined with spiritual healing.
Part of Hurley's spirit was his overweight jolly lovable nature so the island wouldn't want to take that from him but rather embrace it.
Adding to that is how Hurley was a candidate for and later became Jacob's successor - food was a minor character flaw compared to the other obstacles he had to overcome to become this.
My favorite website: http://lostpedia.wikia.com/
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The most obvious answer is that Hugo and the other LOST crash victims were dead the whole time, so naturally he wouldn't have lost any weight.
By the way, I have watched every episode of LOST.
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Has always wondered, in Lost series, the "big" guy by name Hugo did not seem to be losing any weight while on the island. This seems rather impossible considering the drastic change in the amount of labour, walking and his new nutrition plan. Just to remind, he used to be very passive back home and ate a lot of junk food.  So why did he end up not losing any weight (at least visually)?
How did Hugo not lose weight while on the island?
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There are a few reasons to explain Hugo not losing weight on the island. There are a few scenes specifically in the show where we see Hugo overindulging on-island and he had access to the Dharma food stores for a while. However, in reality, the actor is a big man and apparently was told by the producers not to lose weight for the show as the public liked him as he was. In universe again, he was also in charge of food distribution whenever it came up in the show and from his flashbacks we know he has issues with food consumption. Jorge Garcia, the Hurley actor, didn't shed a lot of weight. It is all to do with the fact that he has a significant weight problem, as we'll see. After the crash, total time on the Island was less than four months.
Jorge Garcia, the Hurley actor, didn't shed a lot of weight. It is all to do with the fact that he has a significant weight problem, as we'll see. But in my opinion, this is a mixture of physical and spiritual healing. After the crash, total time on the Island was less than four months. Food was insignificant compared to the obstacles Hurley had overcome to get to become Jacob's successor. It's conceivable that he could gain weight if he had this condition, but it's an exercise in futility to speculate on a medical conditions. He may or may well be doing so because he has the chance to keep it for himself.