Firstly, it won't make a huge amount of difference - you'll still be in debt after uni. Wish I could argue your case, but I had the exact same circumstance at the same point in my life. I kept the day job, and lost the half day. Got a good set of A levels, and went to a good uni. The money I made from my day job helped to keep my head above water, but only just, and I still had debt. I usually had to spend most of Sunday studying, but socialised Fri and Sat nights, and maybe once during the rest of the week.
Ultimately, I suppose your parents just want to make sure you get as good grades as possible so that you actually get to uni.
It all depends on how much of your week is spent socialising, and how much you study. You also don't want to burn out from doing too much of everything.