Was this a bad bet?

9 handed $50 NLHE
I have AKo on the button. 3 limpers when it gets to me and I raise to $3.00 2 folds 1 call. Flop comes 10c Ah 9c pot=$7.25 I bet $4.00 and he calls. Turn comes Ad, he checks and I bet $8.50 and he calls. River is 4d he checks again and I bet $16.00 then he calls and shows 99 for a full house. Should I have just checked the river?

If you had checked, he would have bet more then the 16 you put into the pot which you would have called. You're most likely ahead at the river vs AQ/AJ so get some value. You can only thank him for playing the hand so bad as he did. He turned a FH, but never raised in the entire hand. And this is not a bad beat (he made his hand on the flop).

What'd you mean if I had checked and at which point? (I was on the button)

O wait, I've read it wrong, figured you were OOP. The option to check what I was talking about was the river. I would still have bet the river when in position. He only showed weakness during this hand and 80-90% of the time you're up against a weaker ace or even 2 pair. He played his full house so increadibly weak that you couldn't have put him on that imo.

Ya I was surprised when I saw his hand that he didn't raise me for his last $15. Guess he was afraid I had Aces full.

I think you played it fine. You can't hold off your set on the river just because there might be a full house out there. The chance is really low. I am surprised the other guy didn't raise you on the river... such a pity.