Trouble with a nit min betting 2 streets

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Everest No-Limit Hold'em, $0.10 BB (9 handed) - Everest Converter Tool from FlopTurnRiver.com

MP2 ($14.03)
MP3 ($0.27)
CO ($10)
Hero (Button) ($12.61)
SB ($14.16)
BB ($6.30)
UTG ($5.90)
UTG+1 ($3.30)
MP1 ($2.23)

Preflop: Hero is Button with 2, A
UTG calls $0.10, 5 folds, Hero bets $0.40, SB calls $0.35, 2 folds

Flop: ($1) Q, 2, 4 (2 players)
SB bets $0.10, Hero calls $0.10

Turn: ($1.20) A (2 players)
SB bets $0.10, Hero raises to $0.70, SB calls $0.60

River: ($2.60) 3 (2 players)
SB bets $1.20, Hero raises to $6.20, SB calls $5

Total pot: $15 | Rake: $1

Villain's stats - 6/3/4.0 over 528 hands

PF – Villain’s range is 88+, ATs+, KQs, AQo+ given his VPIP

Flop - I felt justified in calling his min bet as it gives me 11 to 1 pot odds and higher implied odds to hit 2 remaining 2's or 3 remaining A's. 5 outs x 4 gives me ~20% or approximately 5 to 1 odds of hitting. His min bet put him on a range of ATs+, 88+ (not sure if I have grounds to back this up). I saw myself ahead of most of his range (if I hit an A or 2 obviously) except QQ+ and AQ.

Turn – A second min bet confused the shit out of me to be honest. I thought he could be trapping or blocking; without being sure and hitting my two pair, I raised him to about half the pot to see his response (my bet sizing may be off here). His call was even more confusing to me, giving me little info.

River – Since the turn play confused me so much and I didn’t know what to do, I went to my instincts and shoving felt right on the river, as a 5 wasn’t in his range and AA, QQ and AQ are the only three hands beating me. Now that I analyze his river value bet, it seems as if the only thing he could possibly have were hands that beat me, so this is an easy fold in hindsight. However, what should my thought process be here in case his value bet didn’t represent those 3 hands?