Winning Poker, Hold'em No Limit - $0.01/$0.02 - 5 players
Replay this hand on Upswing Poker

UTG: $1.87 (94 bb)
CO: $3.71 (186 bb)
BU (Hero): $2.00 (100 bb)
SB: $1.01 (51 bb)
BB: $1.65 (83 bb)

Pre-Flop: ($0.03) Hero is BTN with A♠ A♦
1 fold, CO raises to $0.05, Hero 3-bets to $0.15, 2 players fold, CO calls $0.10

Flop: ($0.33) Q♠ 2♦ 7♥ (2 players)
CO checks, Hero bets $0.11, CO calls $0.11

Turn: ($0.55) T♦ (2 players)
CO checks, Hero bets $0.42, CO calls $0.42

River: ($1.39) J♠ (2 players)
CO bets $3.03 (all-in), Hero calls $1.32 (all-in)

I read somewhere that folding after putting half of your stack in the pot is a bad plan. However a leak of mine is definitely going broke with one pair.

Without reads on villain I highly doubt this is ever worse value, and it’s hard to come up with ‘natural’ bluffs. Although this matters less, we have lots of better combos to call with as well so we don’t even have to feel that bad about folding - we could feasibly have QQ, TT, all AK combos and even 98s here.

He basically has 0 bluffs, you as well don't have much to fold and this river improves your range and given everything I've said he still shoves, I'd fold this hand still have enough hands to call.

This is a similar spot right:

Winning Poker, Hold'em No Limit - $0.01/$0.02 - 5 players
Replay this hand on Upswing Poker

UTG: $7.66 (383 bb)
CO: $5.36 (268 bb)
BU (Hero): $2.00 (100 bb)
SB: $2.07 (104 bb)
BB: $2.13 (107 bb)

Pre-Flop: ($0.03) Hero is BTN with Q♣ A♠
UTG raises to $0.06, 1 fold, Hero 3-bets to $0.18, 2 players fold, UTG calls $0.12

Flop: ($0.39) 7♠ T♣ Q♥ (2 players)
UTG checks, Hero bets $0.28, UTG calls $0.28

Turn: ($0.95) 7♣ (2 players)
UTG checks, Hero bets $0.68, UTG calls $0.68

River: ($2.31) 9♠ (2 players)
UTG bets $6.52 (all-in), Hero calls $0.86 (all-in)

As you mentioned, have better hands that can call. I guess I just feel more compelled to call because having already invested so much into the pot. In this hand in particular was up against a fish with 53/41 so I figured the 3-bet pre was ok.

Or this hand, also against a fish 56/18 3-bet 23 :

Winning Poker, Hold'em No Limit - $0.01/$0.02 - 5 players
Replay this hand on Upswing Poker

UTG (Hero): $3.69 (185 bb)
CO: $1.72 (86 bb)
BU: $2.21 (111 bb)
SB: $9.63 (482 bb)
BB: $2.35 (118 bb)

Pre-Flop: ($0.03) Hero is UTG with Q♦ Q♣
Hero raises to $0.06, CO 3-bets to $0.10, 2 players fold, BB calls $0.08, Hero 4-bets to $0.50, CO calls $0.40, 1 fold

Flop: ($1.11) K♥ 7♠ 5♦ (2 players)
Hero checks, CO bets $1.06, Hero calls $1.06

Turn: ($3.23) 4♣ (2 players)
Hero checks, CO bets $0.16 (all-in), Hero calls $0.16

it's not how much you invested but what odds your are to call; AQ is very clear call, QQ, you need to make a decision on flop, since it's same as he shoved since you are not folding once you call, so for me it's a shove or fold in that hand, on the flop

Change the plan to something more like "Keep putting money into the pot with good hands until you're given a pretty good clue that it's not going to be profitable to put any more in."
Playing the streets correctly requires constant re-evaluation of your EV.

Don't fall for the sunk-cost fallacy. You should never be committed to stacking off if something happens that suddenly makes it unprofitable to do so.