The phrase ‘big fun’ sounds funny in English. We do not say it. We do not measure the amount of fun we had by using the word big. Fun is not only uncountable in English – we don’t say ‘a’ fun – it is also immeasurable.
We commonly just say, „I had fun.“ If we want to say how much fun we had, we say ‘a lot of fun’, e.g.“ I had a lot of fun at the party“, or we can say ‘great fun’. e.g. „Skiing is great fun.“
Another question I’m often asked is, „What’s the difference between ‘a lot of’ and ‘lots of’? The answer is simple: nothing. You can say both and it means the same. „I had a lot of fun“ or „I had lots of fun“. Just don’t say ‘a lots of’ or ‘lot of’ – these are both wrong!