FT 3 handed. how do you play this?

[lorenz0wns]

My check behind on the turn was to set up the raise on the river. But when he shoved I decided that there were more hands that he shoves that beat me than that didn't. Also I still had 40+ bb by folding

idk about that plan working unless you've done it against him before and he knew you bluffed. it's a really thin value raise on that river card.