Since Sylth's character IS based off of Darth Vader from "Star Wars", that means he WAS a good guy that was turned into a bad guy (but actually still is a good guy just all confusion of what happened in his past) due to beytral and the lost of someone he loved.
So what if Sylth had a wife (that is based on Padm'e, Anikin/Darth's wife), that died cause Tweetums had done something to kill her, and broken-hearted Sylth drove himself insane missing her and wanted Tweetums to pay back for what he had done.
That'll give an explaintion of why Sylth is obsessed with wanting to kill Tweetums (and it aint just for what happened to their ancestors either).
It's true. Even Sylth's name and costume (that hides all the scares and wonds that Tweetums gave him, just like how Darth wears his suit that hides his burned skin) was imspired by Darth Vader (and a bit of the Sith too).
I doubt Sylth had a wife who died. That would just make him a more complicated character, and kidswb apparently doesn't like to complicate characters. Much to the suffering of the fan-base. Sylth is just a character who kidswb thinks we can laugh at and mock.