都正确，只是用法不同：
at the weekends 特指经常发生的,周期性的周末。（比如你经常在周末做哪些事情,而发生的频率很高,就用这个）
at weekend 指一般性的周末，没有特指的意味，只是单纯的表示一个周末。
一、双语例句：
1. at weekends：
They usually forgather at weekends.
他们通常在周末聚会。
The couple enjoys lounging about the streets at weekends.
这对夫妇喜欢在周末逛街。
We should do something together at weekends so as to strengthen our relationship.
为了巩固我们的感情，我们应该在周末一起做一些事情。
You said I could watch more TV at weekends.
你说过我可以在周末多看些电视的。
The next day, on you way to work, you notice that the guy who´s always out walking his poodleat weekends has an even sweeter ride than you.
第二天，你在去工作的路上，你发现那个总是带着他的狮子狗出来散步的家伙在周末的坐骑会比你的还要好。
2. at the weekends ：
When Tom is at home on the weekends, he is at loose ends.
当汤姆在家的时候总是无所事事。
About two-thirds are younger people aged 20 to 32 from wealthy families while 10-20 percentare older auto enthusiasts who drive their supercars mainly at the track on weekends.
其中三分之二的买家是20到32岁的富二代，百分之十到二十的买家是老一辈的汽车爱好者，他们会开着他们的超跑在周末到赛道撒一把。