Calling all-ins v Pushing all-in

We had an interesting discussion regarding All-in EV in my post a few days ago here, and that it doesn't take account of fold equity. I played a relevant hand today where I thought some of the ideas may make my own thinking a little clearer of how I act in these pots, with regard to FE.

Villian is a standard aggrodonk running at 35/25 with 11%3bet, and (naturally) a big loser at both 50nl and 100nl over a large sample.

$0.50/$1 No Limit Hold'em Cash Game, 5 Players
Poker Tools by Stoxpoker - Hand Details

Hero (MP): $133.20 (133.2 bb)
CO: $25.70 (25.7 bb)
BTN: $17.50 (17.5 bb)
SB: $103.45 (103.5 bb)
BB: $135.80 (135.8 bb)

Pre-Flop: Hero is MP with 6 6
Hero raises to $3.50, CO folds, BTN calls $3.50, SB folds, BB calls $2.50

Flop: ($11) 3 7 6 (3 players)
BB checks, Hero bets $8, BTN folds, BB raises to $25, Hero raises to $129.70 and is all-in, BB calls $104.70

When he raises, I think he thinks he is committing himself to the hand. No preflop 3bet from him seems to me almost certainly to be either an unlikely set, or much more likely, a draw, due to the nature of the board. So lets think about things from his scenario for 1 moment. What could I have, that I shove over his check raise? Well I am going to be generous to him and include in my range overpairs from AA-JJ, which, on a bad day for me, I may indeed shove here. I could also have 77-66,33,AcJc,AcTc,9c8c,5c4c. Against this range he is 36% (see the spoiler below if you want to know what he had) and the pot odds are offering him 39%. But we were 135bb deep at the start of the hand. Similarly, and usually, I may be just folding the overpairs, which only gives him 26% equity. Would you call here?

Now lets switch that around. Lets say he donk bets 8bb, I raise 25bb, and he shoves 104bb over the top. Now factoring in the fold equity it becomes a far more reasonable play. Because I must include all sorts of mega combo draws and the 77 that crushes me in his range, making me only 54%. I still always call here against this particular opponent, but I am feeling sick.

But back to the scenario, him calling the allin with such mediocre equity, especially at these limits, seems pretty spewy, especially when you take account of the type of opponent I am (a shove from me usually means something, especially to even aggro-donk regs such as him)

Finally, by building the pot with the CR, when he is deep, he is just setting himself up for difficult decisions on later streets.

Turn: ($270.40) 5 (2 players, 1 is all-in)
River: ($270.40) 5 (2 players, 1 is all-in)
Results: $270.40 pot ($3 rake)
Final Board: 3 7 6 5 5
Hero showed 6 6 (a full house, Sixes full of Fives) and won $267.40 ($134.20 net)
BB showed Q K (a flush, King high) and lost (-$133.20 net)