You are getting 11:1 on the river.
If an A hits his possible hands
uts
AA:1, KK:3, QQ:3, JJ:3, TT:6, AK:2, AQ:3
He wins: 10, you win:9 You tie:2.
Based on his betting and his smile he is most likely to have JJ or AQ. However, he could also have TT and have been smiling because he just took away 3 of your outs. Likewise, KK is possible too.
I would call an A with a bet on the river.