10NL, AK facing turn min-raise

Im trying to understand why we bet the turn knowing we are WA/WB (unlikely WB) and were calling a river bet on 90% of the deck.
Surely if we bet the turn its with the plan of bet/folding?

Interesting hand.

I'm fairly new to poker, and this is the type of hand i often have trouble with. Bear with me when I ask these dumb-ass questions.

Firstly, is our flop bet a bit small here? I would have thought $1.30-$1.50?

Secondly, for those more versed in 3-betting ranges than myself, are TT/AT/88 in a 30/20 villain's possible 3-betting range here?

Unless villain is a complete donk, I tend to fold these spots on the turn... but I can be a bit nitty...