PokerStars No-Limit Hold'em, $0.10 BB (8 handed) from (Format: FlopTurnRiver)

Hero ($10.80)
UTG ($3.45)
UTG+1 ($4.65)
MP1 ($11.80)
MP2 ($8.45)
CO ($10.05)
Button ($8.45)
SB ($9.35)

Preflop: Hero is BB with J, 4.
UTG calls $0.10, UTG+1 calls $0.10, 3 folds, Button calls $0.10, 1 fold, Hero checks.

Flop: ($0.45) J, 4, 8 (4 players)
Hero bets $0.4, UTG calls $0.40, UTG+1 raises to $0.8, Button calls $0.80, Hero raises to $2.5, UTG folds, UTG+1 folds, Button calls $1.70.

Turn: ($6.65) 7 (2 players)
Hero bets $2, Button raises to $5.85, Hero ?

folds to the straight

I need to know how to play unraised pots in the BB more. After looking at my PT stats, my biggest leaks are in the BB then SB. I now fold more in the SB, but what do I do in the BB when I flop TPTK, bottom 2 pair, top 2 pair, etc...

In this case, I folded because i strongly believe he had the straight

You need to realise that none of those hands are monsters. TPTK or top and bottom aren't huge money makers. Check your stats and see if you're winning with One pair and Two pair (under the "misc stats" tab). They are fine to bet with but can't really stand a raise against anything but an overaggressive opponent.