Hero calls $0.20

Turn: ($1.05) 8 (2 players)
Hero checks, Button bets $1.16,

Tbh b/f seemed out of the question as it leaves me committed if he shoves, and when he over bets the pot and basically puts me all in I'm thinking if I can include JJ/TT and maybe A9 in his range it should be an ok call.

Thoughts?