Player seems weak-tight thus far and I've been beating on him a bit in the blinds.

Does anyone ever just call these bets considering they're so grossly weak and small. I mean, it's a pretty cheap price to find out what he's taking this line with and since he's sitting to my left I'd like to get to know him better. Who cares if he has a pair, I'll know exactly what hands he won't reraise me on early streets.

Basically I'm asking who thinks it's worth calling for information or to pick off a (very unlikely and poorly played) bluff.

My reason for 2-barrelling was I wanted him to fold out any mid-pair type hands in fear of the queen. He was like 14/3 so far so I felt he's meek enough to do it.

So to sum it up, I know I'm beat but getting such gross pot odds he may do this with nothing at least some of the time, so by paying for this information now I'll be able to detect what his bets in later hands mean.

PokerStars No-Limit Hold'em, $0.10 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Button ($10)
Hero (SB) ($15.85)
BB ($10.70)
UTG ($14.95)
UTG+1 ($22.25)
MP1 ($4.45)
MP2 ($1.85)
CO ($13.80)

Preflop: Hero is SB with A, J
6 folds, Hero bets $0.40, BB calls $0.30

Flop: ($0.80) 2, Q, 4 (2 players)
Hero bets $0.50, BB calls $0.50

Turn: ($1.80) 7 (2 players)
Hero bets $1.30, BB calls $1.30

River: ($4.40) 10 (2 players)
Hero checks, BB bets $1, Hero calls $1

Total pot: $6.40 | Rake: $0.30