Just started playing the opponent, absolutely no reads. You just get it in here?

Full Tilt Poker $0.25/$0.50 No Limit Hold'em - 2 players - View hand 43376
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BB: $216.65
Hero (BTN/SB): $51.00

Pre Flop: ($0.75) Hero is BTN/SB with 8 A
Hero raises to $1.50, BB calls $1

Flop: ($3.00) 7 8 4 (2 players)
BB checks, Hero bets $2.50, BB raises to $10.50, Hero calls $8

Turn: ($24.00) 7 (2 players)
BB bets $16.50, Hero...?

I'd shove. There's not much that beats you since he probably 3bets most overpairs. He's repping a set/56/ imo. That's a pretty tight range, I'd expect to get called by alot of draws if you shove.

shoving is probably fine

Yea this is kinda what I thought, there's a ton to semi-bluff on this board as far as draws/combo draws, and he could be doing this with worse 8s. I feel like he's not doing this with many 7s, and I feel like he'd be 3-betting 9s+ most of the time too. Just hate spots like this early in the match where I have no idea whether I'm crushing the villain's range or getting crushed.

He´s never doing this with an 8 and he´s only repping 56 or a boat.
The only 7 he can have is 78/47 and i doubt he has an overpair.
I would lean more like a fold because pushing is much higher variance
and you have no reads, if he have a flushdraw i assume he will check
that back at least half the time.
It´s really close though, since you have no reads..

Is it worth 3betting this flop? Given the texture Villain could have a lot of pair + gutshot type hands that might not fold/are worth folding out anyway.

Turn - Shove, but it could be closer if the suits were different. Since Villain can't have a 7 and a flush draw (or even a 7 and a bdfd), Villain's range won't contain that many 7s. Villain can't have an 8 and a flush draw either (since you hold the 8d), but since 8s will be more likely to raise the flop than 7s anyway, the effect isn't as significant.

W/o reads I think it's a bit marginal to get it all in on the flop since there is a ton of stuff we're flipping with/dominated by, I think I fold on a ton of turns if he keeps up the aggression just because I have no read. This turn is pretty much the best I could get since no flush/straight cards came, and it makes his 2-pair hands less likely. I definitely agree it'd be way closer if the 7 was off suit since, like you say, the pair + FD combo's just tripped up. I actually didn't think of the 8 of diamonds killing his pair + FD outs, but that takes away some of his big draw combinations, but that's kinda bad because that takes out a big part of his range that we're dominating/he's not folding.

Anyways, I feel like the range of hands he's representing on the flop that crush us on the turn is pretty slim compared to everything that we're way ahead of now, and since we're 'only' 100BB and I called the flop, I can't really fold that turn too much. So I ended up getting it in and he had A4o for bottom pair no draw

Early on in a match with no reads I fold some of these spots because against his check raising range we are almost never in that great of shape. He has alot of combo draws which is doing great against our hand, and so many cards are scare cards for us. Its alittle nitty to fold that flop but its such a high varience situation that I think folding and losing a small pot early is more +EV. There are so many times I lose a stack in situations like this where 30 minutes later I realize he is almost never bluffing in spots like this.

As played the seven is really on of the best cards in the deck if we are continuing with the hand, so I would just shove.

The thing about this board is that it's drawy heavy without really having that many better made hand combinations. 87s, 65s and 44 are the biggest worries, as 77+ gets proportionally more likely to be 3bet, and 84s/74s/87o are weak enough that there's a strong chance they'll be folded preflop. Also, A8 is in relatively strong shape against a reasonable number of hands like Ax and weaker 8s.

I wouldn't 3b my overpairs early in the match so you can't discount them
I don't see why villain can't be raising 76s on the flop either because he has mid pair + gutshot

not saying we should fold, though