I am trying to understand this question. Does it mean to find some time to spend during the weekend, or does it mean to go through it, as to make it go away?
In colloquial language:
Ну давай when it precedes some action means "let's" or "then let's". Example:
- Ну давай колодец починим, - раздражаясь, сказал капитан. (Ю. И. Болдырев "Приключения Васи Куролесова")
"Ну давай колодец починим" means "then let us repair (your) well".
тогда means then.
когда-то на выходных means at some time at weekend
пересечёмся on young people's slang means встретимся (meet in plural and future tense)
So, the whole sentence means "then let us meet some time on weekend".
"Ну, давай" usually means "so long, bye". "Пересечёмся" ("we'll cross [each other's way]") is slang for "we'll meet". The whole phrase is very colloquial bordering on teenage slang for "See you later, hope we'll see each other at weekend". "Выходные" is "weekend".
The whole phrase means "Bye, I hope we'll meet at weekend some day".