Aged 26 you won't have any problems getting the NPPL medical. Its a declaration that your GP signs, usually without even examining you, and its basically a bit of paper that means he is unaware of anything in your medical history that will incapacitate you whilst you're flying.
An LAPL is a bit closer to a class 2 medical in that there is a proper examination, with various prodding, poking and measuring and checking your wee for evidence of diabetes. If you manage to get your weight down to 15 stone then at your age there won't be a problem in passing this.
The LAPL is something to be aware of because to fly EASA aircraft(Cessna 172, PA 28 and most other stuff with a CofA rather than on a permit), which is what the majority of hire aircraft will be, you'll need an LAPL beyond April 2015. If you're still on the large side by then and you're hiring club aircraft to fly in, then you'll definitely need an LAPL. However, if you go down the 'permit to fly' based aircraft route then you won't need an LAPL and will probably spend less per hour on your flying.
FYI, an NPPL SSEA can be converted to an LAPL with only the need to pass the medical and submit the form to the CAA.