wow - that's a hard spot to be in. If he is used to roaming - then being kept at home is likely the major contributor towards his anti-social behaviour. (my male cat gets like that when he is kept home). It seems a shame to have to give him away just because someone else if feeding him though (although I certainly understand your concerns regarding his health). Could you possibly tell them a white lie and tell your neighbour that he is really a sick cat (cat aids or something) and that he can only eat the special 'perscription' cat food you get from the vet? They might take you more seriously if you are concerned about something more then just being 'overweight' - IYKWIM. Otherwise, have you got the room to install a cat run in the backyard - you wouldn't have to use it all the time, you could let him roam occaisionally, but have him in the run more often then roaming to give him a chance to stick to his 'diet' and yet still have an area to play outside.