Learn English – “On the weekend” or “during the weekend”

I have to admit I haven't consulted any sources, but here is what I'd say is "correct":

• On Saturdays, her sister Ann usually comes to stay with Mary for the weekend.

and

• What are you going to do for the weekend?
• What are you going to do over the weekend?

and

• We are going to Paris for the weekend.
• We are going to Paris over the weekend.

"Weekend" would not normally be pluralized when preceeded by the word "the". For example:

• Are you going to stay here on weekends?

And finally, to address "at the weekend": this is often seen in British publications, but I've never seen the phrase "at the weekend" in American English.

It really depends on the situation.

But if you're just asking about grammar, all of your sentences are right and in use except A, B and G.

These are the reasons:

1. "at" and "on" are both used. The former in British English and the latter in American.

2. Cambridge Dictionary recognizes "at weekends" but not "at the weekends."

3. It isn't always so but "the weekend" refers to a specific weekend while "(the) weekends" means every weekend.

With the last, you can determine which one is "better" depending on your context.

Sources:

Cambridge Dictionaries

Merriam-Webster Learner's Dictionary