dregal, let me explain why

Say I had K,Q and I'm the opponent, if you make a small bet on the turn, when you check on the river I'm going to think your hand is fairly weak. I will not want to just check and give you a showdown for free. I feel I have the best hand and I will want to make a value bet since you called my raise on the turn, however I will not want to bet too much and get you to fold quickly, by checking on the river you will make me fearful that you will fold to anything but a small bet.

This is why you should check, because than you will see the $45 bet that you made on the river only you'll get to find out if you win the pot or not with that bet,