Is there a way to find about the user who blacklisted you?

nope and that's the exact reason why - because it's up to them to decide whether they want to be bothered by you adding them and asking why you got BLKed, asking for BL removal etc. If they want to they could inform you you got BLed and for what reason. If SG gave info about who BLed you you can bet hundreds of salty kids would just straight up harass/spam/beg whoever BLed them for unBL.

Also whoever BLed you will also not be able to enter any of your GAs as well with a new system, so there's even less reason to know who BLed you exactly. Just don't bother with it - getting BLed is part of SG, there will always be someone who BLs you for whatever reason.

Believe it or not, there is a lot of people who will BL you for any stupid reason. For example: Just for asking these, you will be BL again by some idiot.
The best you can do is learn to ignore them, and assume that every time you post something, you might get BL for no reason at all. You might find out who BL you while trying to enter a giveaway a receiving a message saying you where BL by the user, then you can decide what to do. I would investigate or ask him/her why, if no answer is given or has a crappy attitude, I BL them back. Simple as that.

In my case, I get BL sometimes just for posting giveaways with a puzzle or jigsaw.

Maybe something you've said or just your name. People nowadays get offended by anything.
ESGT has a whitelist/blacklist checker (has lots of features), but haven't tried it.

yes, use scripts to scan blacklists/whitelists (it's not against the rules ^^).
https://www.steamgifts.com/discussion/Zevqn/

You can counter them by clearing out your BL, since it is reciprocal.

The 9th person to blacklisted me was on my b/day... Now the 10th person blacklisted me. I don't care.

There can be any reason or no reason at all. You'll get used to it. I reached the point where I couldn't care any more when I was blacklisted (and reported) a year and a half ago for creating too many giveaways.

Unless they got offended by one of your posts, the only reason I can think of would be some frustrated users that didn't win one of your games, because you only create level 0 giveaways.
For what it's worth you are on my whitelist now.

Also now that blacklisting works both ways, I really don't mind getting blacklisted by some random angry kid with a terrible ratio.

Getting blacklisted is annoying at first, though the effect wears off over time. Think of this way: there are over 1 million registered users on this site. You will need to use scientific notion to grasp how minuscule the non blacklist to blacklist ratio is.

There is a script for it. I don't care about it now, I'd say 99% of the ones I've seen I wouldn't enter any of their giveaways so I'm hardly losing out. Plus, if they do a wishlisted giveaway or are the 1% then I'll just buy the game if I want it so desperately xD

Only once have i joined a GA from someone who blacklisted me and it was because i missed to say thanks in a GA i won. Understandable but quite the detective work he had finding that one. He later removed me and i haven't had any problems since that.

Be happy, being on any list means you were noticed at all :)