I suppose this question has been done and answered to death, including here on this blog, but theres a very very simple reason why obese people regain weight, and its EXACTLY the same reason that they got to their obese state in the first place.
I recently watched this excellent video by Brian who describes his theory of the "sponge syndrome" which is basically just another way of phrasing what I have been trying to say here on this blog. I.E. obesity involves recruitment of stem cells in adipose tissue called "pre-adipocytes" which morph into fully mature adipocytes and accumulate fat. And diet/exercise DOES not cause them to un-morph back into fat-less stem cell preadipocytes.
The reason reduced obese regain weight is exactly the same reason they got fat in the first place, with induction of adipogenesis in pre-adipocytes, ( adipogenesis being the phrase meaning the pathway of a pre-adipocyte morphing into an adipocyte ) the activity and load of enzymes involved in triglyceride synthesis increase massively, its been described here
When cells of the established preadipose line 3T3-L1 enter a resting state, they accumulate triglyceride and convert to adipose cells. The adipose conversion is brought about by a large increase in the rate of triglyceride synthesisand this
Glycerophosphate acyltransferase activity rises sharply during the conversion and reaches a level of 80 times higher than that of another 3T3 subline in which practically no adipose conversion takes place
And I blogged here about this.
So... a pre-adipocyte stores no fat.... CICO is irrelevant
Suddenly adipogenesis pathway activated, lipogenesis gene's switched on, Glycerophosphate acyltransferase activity rises, and Triglycerides accumulate........ again CICO irrelevant.
Go on a diet and exercise heavily, empty most of your fat cells to a smaller volume, but guess what, the excess adipocytes are still there, and because the excess number of adipocytes are still there.... excess amount of Glycerophosphate acyltransferase activity IS STILL THERE.
So guess what happens with time as Glycerophosphate acyltransferase activity remains elevated? Triglycerides ( fat ) accumulates again, and you regain weight.
Its really not hard at all.
P.S. I know Glycerophosphate acyltransferase is not the only enzyme involved in trig synthesis etc. Im just picking it out as an easy to understand example.