Question: Can you push [Tenser's Floating Disk](http://www.5esrd.com/spellcasting/all-spells/f/floating-disk/) so that it doesn't just hang out behind you? If so, how hard would it be to push?

Answer: 
No
==

It isn't described as having any weight, but it is described as immobile in it's description, at least while it is within 20 feet of you.
Immobile could mean it stops moving on it own. It could mean nothing can ever move it.

This really is not something the RAW answers. No amount of interpretation will make this clear. There is no way of parsing this that will be immune to abuse.

If you take immobile to be an absolute you've just given the player an immovable object to counter the DM's irresistible force. They could stop a charging dragon with one of these and build a cage with three of them.

So don't think being conservative with how you read a spell makes it immune to abuse.

Tenser's floating disk is fun because you can invent uses for it. A DM that insists the only use is to escape the encumbrance rules is running a poor game. 

The best way to answer this question is to go buy a scroll of Tensor's Floating Disc. Use it. Give the disc a push. See what happens. Now decide if you want to learn the spell.