Hi Mary! Both these phrases have the same meaning. In the US we say 'on the weekend'. However, I work with people from England and New Zealand and they use 'at the weekend'. As I tell my students, use the form of English that you're comfortable with if you have a choice between American English and English. :) I hope this helps!

"At the weekend" is the more commonly used phrase, as far as I know. Come to think of it, I can't remember any instances recently where either myself or someone else has said "on the weekend" as opposed to "at the weekend". It may even be that "on the weekend" is just straight up wrong, since 'on' implies direction or whereabouts, whereas 'at' suggests a time. "What are you doing at the weekend?" "At what time is your doctor's appointment?" - "My doctor's appointment is at 3."

On the weekend is mainly used in the USA and Canada, while at the weekend seems to be used in Ireland (I'm Irish) and the UK. I'm not sure what people from Australia/New Zealand etc. would say.