What would you do? #55 - Facing river shove on scary board

Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 7 players
The Official DeucesCracked.com Hand History Converter

Hero (BB): $69.35
UTG: $50.00
UTG+1: $39.80
MP: $14.85
CO: $16.75
BTN: $74.75 - 15/12 @ 266 hands
SB: $50.25

Pre Flop: ($0.75) Hero is BB with 8h 7h
2 folds, MP calls $0.50, 1 fold, BTN calls $0.50, 1 fold, Hero checks

Flop: ($1.75) 4h 5s 5d (3 players)
Hero checks, MP bets $0.50, BTN calls $0.50, Hero calls $0.50

Turn: ($3.25) Ts (3 players)
Hero checks, MP bets $0.50, BTN calls $0.50, Hero raises to $2.75, MP folds, BTN calls $2.25
It seems like a fairly passive hand, let's find out whether I can steal this sucker. I still have a live inside straight draw.

River: ($9.25) 6c (2 players)
Hero bets $7, BTN requests TIME, BTN raises to $71 all in, Hero requests TIME, Hero folds
Completes the straight. Keep in mind that this is a limped pot. Is anyone in their right mind making this call? I don't understand what the BTN could have here, 34 is certainly a limpable possibility, but is 44 or 66? Against a 15/12? I don't think I can call this bet on a limped pot where I have no hand to put him on. I gave him huge credit!

Is anyone calling for a total ~150 BBs (keep in mind that I'm deep stacked here)? Is this a bad lay down?

Final Pot: $23.25
BTN wins $22.10
(Rake: $1.15)