Ivyun, "On weekends" is the correct way to say that you participate in something on most Saturdays and Sundays. It would be incorrect to say "on weekend." Rather, you could add the article "the" and say "on the weekend" and be correct. In this instance, "on the weekend" generally refers to only one particular Saturday and Sunday. For example: On weekends, I spend time with my parents in the countryside. I plan to spend time with my parents on the weekend. I often spend time with my parents on the weekends.

Ivyun, "on weekends" implies habitual, repeated action. For example, in summer we go to the lake on weekends. I would not say "on weekend". I might say "on the weekend", which may also imply habitual action. For example, in summer on the weekend we go to the lake.