25NL - TT overpair, facing resistance

[The Mayo]

I have no reads. This is within my first 10 hands at the table. Villain hasn't done anything that has drawn my attention.

I feel like I misplayed this, but I don't exactly know where. By the turn, it was pretty obvious to me that I was beat.

Note: Flop bet was a misclick. I intended to bet $4.

Should I have folded to the flop minraise? The 3bet preflop? Or should I have stayed in the hand and gone to the felt with my overpair? My analysis, once the turn bet comes, is that villain has a big pocket pair. I'm confident that that's the case, but could I have figured this out any earlier against an unknown?

Poker Stars - No Limit Hold'em Cash Game - $0.10/$0.25 Blinds - 3 Players - (LegoPoker HH Converter)

<font color="black">HERO (SB): $36.25</font>
<font color="black">BB: $25.40</font>
BTN: $18.50

<font color="black">Preflop:</font> HERO is dealt T[img]/images/graemlins/spade.gif[/img] T (3 Players)
BTN folds, <font color="red">HERO raises to $1</font>, <font color="red">BB raises to $2.50</font>, HERO calls $1.50

<font color="black">Flop:</font> ($5) 4 2 2[img]/images/graemlins/heart.gif[/img] (2 Players)
<font color="red">HERO bets $2.75</font> <font color="green">[misclick]</font>, <font color="red">BB raises to $5.50</font>, HERO calls $2.75

<font color="black">Turn:</font> ($16) 4[img]/images/graemlins/spade.gif[/img] (2 Players)
HERO checks, <font color="red">BB bets $5</font>, HERO folds

Pot Size: $21 ($0.75 Rake)