Start off slow and just keep building up your exercise gradually. I've been doing MMA and BJJ training for a couple of months and have dropped about 16lbs already (down from close to 14 and a half stone at the start of july - The regular training as well as a complete changing diet. Cutting out fizzy drinks and sweets and replacing them with water and fruit has been the main factor.
If you have been in combat sports shape in the past it won't be as hard to drop those pesky extra pounds as it would have been if just overweight with no training experience. I'd suggest dropping some weight before going back to Muay Thai otherwise you'll gas right away.