You may be referring to two words. "Weekend" is the word that refers to Saturday and Sunday, the two days at the end of the working week (years ago, many people worked Monday through Friday, so they looked forward to having those two days off). But you may be referring to a word that sounds very similar-- "weakened"-- this is an adjective, referring to becoming weaker, feeling not very strong.
You can't say "At the Weekend", it's not proper english. You can say "on the weekend" if you mean, for example, "we can't go to Disneyland today, but maybe on the weekend we can."
last weekend
this weekend I'm going ...
The weekend had its ups and downs.
2 days in a weekend Two days in a weekend
The weekend of the week you are currently in is this weekend, Next weekend would refer to the week after that. Then of course it depends on who you are talking to, If you came up to me on monday and said lets do something next weekend, I would assume you mean the very next weekend. If you said the same thing on friday I would then assume you mean the weekend after this coming weekend. Confused? That is why I end up saying things like two weekends from now, or the weekend after this. Unless you know how the other person thinks you can not be sure so clarify.
the same as in English
What do you do at the weekend?
What do you like to do during the weekend
The weekend. Sometimes used to indicate Friday evening as well.
The weekend.
Family Weekend