"Weekend" means the two days at the end of the week, Saturday and Sunday. Saturday by itself is not a weekend. Saturday is just one day of the weekend. However, because Saturday is part of the weekend, if something happens on Saturday, you can say that it happens "on the weekend." The usual phrase for describing something that will happen on Saturday or Sunday (or both days) is "on the weekend." Say "on THE weekend" if you mean the current weekend (it's happening now, or is about to happen). Say "on A weekend" if you mean some weekend in the future, or you don't have any particular weekend in mind ("let's plan to have the party on a weekend in June"). You can't say "at" the weekend. Sometimes people will say that something is going to happen "at week-end," which is slightly different. It means that the thing will happen at the end of the week (which could mean Friday if the person is referring to a work-week). The usage is similar to "year-end" ("There will be several year-end celebrations in this area." The celebrations will occur at the time when the year ends.) You can say "weekends" in the plural. It means more than one weekend. There are usually about four weekends in every month. "In summer" and "in the summer" mean basically the same thing. In most cases they are interchangeable.

There are differences in usage between British and American English. We use slightly different phrases. By the way, Sunday is not technically part of the weekend; Sunday is the first day of the week. In normal English, however, everybody thinks of Sunday as part of the weekend. The work week starts on Monday, but the actual first day of the week is Sunday.

Just to correct Gray's US-perspective answer, where she says "You can't say 'at the weekend' ". In fact, you CAN say 'at the weekend'. Millions of us say it all the time! This is the normal way to say this in British English. 'At the weekend' can refer to the coming weekend, as in "What are you doing at the weekend?'. 'At the weekend' can also refer to weekends in general, as in "We're a bilingual household. We speak English during the week and Spanish at the weekend". You could also say 'at weekends' in this context. To me, 'at weekend' doesn't sound natural. Well, it does - but I've been told many times that it isn't right. In the corner of England where I grew up, we said 'at weekend' as a regional alternative to the standard 'at the weekend'. When I went away to university, my well-educated friends mocked me for saying 'at weekend', and I soon learnt that the correct expression was 'at the weekend'. 'On the weekend' is not natural for most BrE English speakers, but we are used to hearing it from American media. It is becoming more accepted now, especially among younger speakers. As you can see, and as Mr Rerum pointed out, there are differences in usage with the word 'weekend'. Not with seasons, however. 'In' is the standard preposition with 'summer', and the 'the' is optional. I don't think that there is a significant difference between 'in summer' and 'in the summer'. We tend to use 'in the summer' to refer to a particular summer ( such as the coming one), but we also use 'in the summer' to talk about summers in general. 'In summer' usually means summers in general, but it would be fine to use it to refer to a particular one.