Preflop: looks like Hero is trying to protect his hand (4x raise) which is strong at the moment but vulnerable post-flop. I'd say there are a lot of 66-99, A7-A9, QJ-QT, KJ-KT type hands in his range.
Flop: Hero checks, so that means:
a) he missed the flop
b) he hit the flop big and wants to extract the bluff.
I think b) option is unlikely, because check from preflop aggressor on THAT flop is much more suspicious that a regular cbet on A hi flop.
Turn: since BU checked back the flop, Hero may think BU is not interested in that pot so he tries to steal it by delayed cbet.
River: BU calls turn cbet and Hero decides to give up but faces an unusual bet size of the BU. In my opinion it's too big for value bet on that board. If BU had a strong flush he would make a thin value bet. If BU had a weak flush he would check back. If BU had a good looking but weak hand that can still win, like two pair or set, he would definitely check back. So by BU's bet sizing Hero decides that BU is bluffing with air and since Hero doesn't have a proper bluff catcher, he decides to ship it.
My guess: I think Hero doesn't have the following for sure: Ax, Kx, 8x, 99+, or any Spade. I rule out QJ ant QT because I think Hero would cbet the flop with these. I doubt Hero would 3bet 44-55 preflop, so I'm left with 66 and 77 no spades. That's a 50/50 guess, so let it be 77 no spades.