Do you go to bed late at night or get out of bed late in the morning? Also are you wanting to speak American or British English? I would think the sentences should be. 1. I go to sleep late at/on weekends. 2. I wake up late at/on weekends. I can't answer fully until you have answered my first question.

I think we use "at the weekends" in British English.

The correct one is #2. “Sleep late” means “get up late.”

for American English ok Good on the weekend (I am not sure if they use singular weekend or plural weekends) for British English at the weekend is how we say it. It is the major thing we disagree about and both agree mutually to disagree about it.