I think all the flop raise does is "find the ace".
Once you found it your only hope was that he's weak enough to fold top pair if his kicker is weak as well. The only way to achieve that is to bet again on the turn.
When you checked behind, he HAS to call your river bet.
Notice that you lose the same amount by betting turn, checking behind on river and give yourself a (small) chance to steal the pot from unknown player.