Are these phrases interchangeable?
1. over the weekends
2. at the weekends
3. during the weekends
4. on the weekends
Sample sentence: I love to read books on the weekends?
I would also like to thank emsr2d2 for sharing the difference between BrE and AmE when it comes to at/on.
As for the others, I would say that "during the weekends" and "over the weekends" imply activities that last for some time, such as golfing or playing in rugby matches. Reading the newspaper or doing the food shopping would tend to be shorter, I would think, and thus call for at/on. Reading books could go either way. I have younger students who certainly read books "during/over the weekends!"