Really?
What would somebody put me on if I'm betting like this?
Did the check look like weakness to them perhaps?

Anybody else ever been in a similar spot (or had the AK in this/similar spot?)

The only thing I can think is that they were planning to bluff me on the river, except they weren't the ones betting first?

Full Tilt No-Limit Hold'em, $0.25 BB (6 handed) - Full Tilt Converter Tool from Poker Strategy Forum | Online Texas Holdem Reviews Strategies Tools & Bonus Guide

Button ($26.18)
SB ($26.37)
BB ($25)
Hero (UTG) ($38.86)
MP ($21.27)
CO ($29.59)

Preflop: Hero is UTG with 4s, 4c
Hero bets $0.85, 1 fold, CO calls $0.85, Button raises to $3.39, 2 folds, Hero calls $2.54, 1 fold

Flop: ($7.98) Qh, 5s, 7c (2 players)
Hero checks, Button checks

Turn: ($7.98) Qd (2 players)
Hero bets $6.25, Button calls $6.25

River: ($20.48) 3d (2 players)
Hero bets $20.48, Button calls $16.54 (All-In)

Total pot: $53.56 | Rake: $2.67

Results:
Button had Ks, Ac (one pair, Queens).
Hero had 4s, 4c (two pair, Queens and fours).
Outcome: Hero won $50.89



p.s - I know it's disgusting to have 44 in that spot and bet - I usually wouldn't, not sure what I was thinking that day...

you take a fishy unbalanced line and get called by a bluff catcher, what's the question?