You can’t force it, period. I can all but guarantee his brother’s called him a fatass more than once and busted his balls about being out of shape. That’s a huge reason why he “doesn’t seem like he wants to train at all”.
Nudging him towards any kind of sport, either in school or just recreational, will be just fine. Paintball, handball, rock climbing, competitive dodgeball, anything that’s active will achieve the same goal with less reluctance. And it’ll be his own thing, not something you and his brother are making him do. This is the psychology part of being a trainer.