You don't say much about how you decline, yet this is key. Compare:
We are all having a [event] dinner this weekend, you'll be there of course won't you? See you at 3!
No, I won't be there, I'm busy.
Your sister is coming over this weekend. I think we'll have a bar be que. Are you joining us?
I wish I could! Unfortunately I have 120 exam papers to mark by Monday. I'm going to get on them extra quick so I might be done by Sunday afternoon. I definitely can't come Saturday, and I can't promise Sunday but I can try. I'll let you know how the marking goes.
I wish I could! Unfortunately I have 120 exam papers to mark by Monday. I know from previous marking weekends that there's no way I can get away to come and see you. Maybe next weekend?
You need to express agreement with their basic point that it would be nice to be together. Much of their arguing is of the form "it would be nice to be together. We are sad that we are not together" and so on. Agreeing with this means they can't keep arguing with you about it. You also need to be specific about how busy you are. Otherwise it sounds like a made-up excuse. You have a deadline, something is due, you have to finish something, you made a plan with your sweetheart, whatever. And you regret that this deadline or this existing commitment makes it impossible (not your choice, impossible) to accept their invitation this time. Maybe next time.
When they say "but we won't be happy without you" or the like, all you need to do is agree. Don't try to trap them in some logical flaw and prove they are stupid and doing the wrong thing. Agree with them. "Aw, thanks, that's really sweet. I would be happier if I was able to see you this weekend as well." And if you can, look ahead to a specific time when you are planning to come and see them, and remind them about that future happy time.
Right now, you're wasting time and effort arguing back when they say things like "we will be sad" or "you don't care about us." When you decline these invitations in the way I'm suggesting, you can see that it includes saying you care about them, saying you wish you could visit them more often, agreeing that it would be happier if you were there and so on. This is more pleasant for both them and you.
You also need to remind them that you do not have a normal workload. Most people have their weekends relatively free. They may need to do some errands, or want to spend time with the person they're in a relationship with, but they can spend an afternoon and evening with their parents easily enough. But because you have both a job and your studies, you have a lot less free time than people expect. You will probably have to mention this more than once. For example, look ahead to the time when you will have completed your studies, and will be back to normal for the time you have available. As well, you can share your fears with them.
I am concerned that if I do not do well on this exam (or do not finish my paper, or do not get this report done, etc) I will fail my course, or be fired, or not get the promotion I was counting on, or whatever.
Now you're not being all superior and saying "I have better stuff to do than spend a weekend with the likes of you" you're sharing your feelings as families do, and bringing them onto your team, the team that is making sacrifices so you can earn this degree or excel at this job, or both. You are aligning with them. This can be very powerful and make you feel much more supported and cared for while making them feel accepted and wanted instead of being the people you don't have time for.