flop shove w/ 77 in 3-bet pot

sean asked me to look at this hand he played: 

Full Tilt Poker NL Hold'em - $1/$2 Ring (6 handed)
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Starting Stacks:
Seat 1: SB ($201)
Seat 2: BB ($491.75)
Seat 3: UTG ($427.70)
Seat 4: LP ($607.10)
Seat 5: CO (Hero) ($215.40)
Seat 6: BTN ($200)

Preflop: Hero is CO with 7c 7d
2 folds, Hero raises $7, 2 folds, BB raises $26, Hero calls $19

Flop: ($53) Ad 5d 8d (3 players)
BB bets $45, Hero raises all-in $189.40, BB calls $144.40

the obvious questions are what are the bb's cbetting and calling ranges? the calling range probably doesnt vary a ton across villains; i used {>=tp, fd w/ Td+}.  it's not so easy to estimate a cbetting range, so i included a variable in the range, {>=tp, x% of all other hands}, and varied x from 0-100% to get the following results:

so, basically, we need bb to c-bet >54% of his less-than-tp hands to turn a profit. if we run the ev calc w/ x = 55%, we get ev = +$0.82 and a bb bet/fold range that includes {JJ-KK, 99, KQs/o, QJs, JTs (all no diamond)}.

idk, i cant say i loved the shove at first glance and it's definitely a high-variance play, but after a closer look it doesnt look too bad v. typical TAG regs who cbet a lot.