Preflop spot: shove or 3-bet small?

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Preflop spot: shove or 3-bet small?

Blinds: $0.50/$1.00 (5 Players) BN: $55.69
SB: $191.94
BB: $80.00 (Hero)
UTG: $20.00
CO: $47.47
UTG is weaker player.
Preflop ($1.50) Hero is BB with T T
UTG raises to $3.00, 3 folds, Hero raises to $80.00 and is all in, UTG calls $17.00 and is all in
Villain is weak. I'm assuming that he opens something like: 22+, A9s+, KTs+, QTs+, JTs, AJo+, KQo (13% of hands.)

Rather basic question, but I am unsure of how to handle this spot. Should I shove here, or 3-bet to something like 8.5BB?

The problem with shoving is: I'm investing 19BB to win 3.5BB, which seems a bit excessive.

The problem with 3-betting to 8.5BB is that if he shoves, I'm getting 28% pot odds, so I have to call with almost anything I 3-bet. So I don't really have the possibility of a 3-bet bluff. So I might as well shove.

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