Could you tell me the difference between
We go to a restaurant at weekends?
The preposition at (at weekends) is used in British English.
It means "we go to the restaurant" on all weekends. It does not state a specific weekend (this weekend, next weekend).
The American English version is "we go to a restaurant on weekends"
We go to a restaurant weekends?
We go to a restaurant (on/at - missing preposition) weekends?
The grammar is incorrect because there is no preposition between the noun restaurant and the time weekends. A time preposition is required (on, at).
We go to a restaurant at weekend?
We go to a restaurant at (the - missing determiner)weekend
This phrase sounds awkward and unnatural to me in American/Canadian English. If someone could clarify, would it be appropriate in British English? Either way, because you are only speaking of ONE weekend, you require a determiner for the single noun (the weekend). The word "weekends", used in previous sentences, is a plural noun and does not require a determiner.