I don't think you gain much by betting, if he is on a draw with something like JT he will fold, but you win that pot anyway by checking. I don't think he folds anything that has you beat. I think the only way betting makes you money is if he holds something like A8 and he folds so you win the whole pot instead of splitting. When your best case outcome has him folding a hand you would split the pot with it is not worth all the times he calls and beats you.