I've done one, it was awesome.
I had to raise £200 to pay for the jump and anything else on top of that went to the charity. I paid £100 of that myself, and got generous sponsorship instead of birthday presents from my nearest and dearest, so I didn't feel like I was asking people to sponsor my jolly. Amazing as it was, I was proper shitting myself before hand, and I raised £2500 on top of the cost of the jump. This was before people started to get charity fatigue though.
There is a fat limit, but it's huge. You do need to be weighed, but a slightly knackered back shouldn't be a problem, just let them know. I know three severely disabled people who have done it, so I wouldn't have thought a bad back would be a huge issue. It won't kill you, but on the day I did it, one person did break their leg on landing. But that was because he didn't follow instructions.
There are other ways of raising money, obviously. But they nearly all involve asking people to part with money they woudo have otherwise spent elsewhere, so this is as good a way as any.