4-handed 10NL on Unibet. Co was aggressive and loose from LP

Hero is BB with A3o

Co opens 30c and it folds around to me in BB and I make it $1 as a bluff, Co calls.

Flop
pot ($2.05)
2s Qh 4h

Hero: bets 1.30
Co: calls

I felt this was a dry enough board to try push him off some under pairs, and random suited Broadway that don't have a queen. When he calls I feel he may have, 99-QQ, KQs,AQ+

Turn
pot ($4.65)
Qs

Hero: bets 2.90
Co: calls

*I liked the queen on the turn as it reduced his chances of having one so I bet again, plus I have my gutshot as insurance. I try to get the unders and some combos of AK to fold. Should I be giving up here? *

River
pot ($10.45)
5c
Hero: jams around $5

A pretty easy jam OTR considering I now make my hand and it looks very likely villain has a queen, I also only have half a pot bet.

I feel I over played this, should I be betting smaller on some streets and just giving up on others? thanks