pocket 4s in the blind

in a $10 buy-in tournament on Party (1st: $1400), I had 44 in the BB. No one raised, and 5 of us saw the flop of A, 9, 4, with two hearts.
On a rainbow board, I'd be inclined to check, looking to check-raise an ace, but with the two hearts, I didn't want to risk a free card, so I bet the pot.
One player called.
The turn was the duece of hearts.
I bet the same amount I had bet on the flop; he flat-called again.
The river was an ace; I bet 80% of the pot.
He thought for a long while; I figured he had an ace, and that he was very worried about the flush.
He called, and fours full were good.

I made a small bet on the turn for information. If raised, I would have had a tough decision, depending on the size of the raise. I felt that a check would have put larceny in his heart, giving him a chance to bet me out of the pot. A small bet, I hoped, would either just be called or he'd fold, fearing flush. If he had a flush, he might just call, figuring I would fire again on the river and he could raise me there.

He didn't show his cards, so I can only guess at his hand. I figure he held an ace, and hit the one card that would compel him to pay me off in case I was bluffing without the flush; little did he know I was full.