1.Which day do you want to see the girl?
2.I want to meet the girl this weekend.
3.I only have time on weekends,you don't come to see me on ordinary days.
4.I will be off tomorrow,let's fish/let's climb.
5.这三个词组都是对的.on weekend 是“在一个周末”.on weekends是“在许多个周末”,用的是复数形式的.而on the weekend是指“（指定的)在一个周末".
at the weekend和 at weekends都是错误的,weekend或weekends前用介词on不能是at.
希望我的回答能对你有帮助.——一位酷爱英语的学生啦