I haven't read all the replies but here is my .02:
I don't know anything about the family dynamics at work here so this may all be invalid depending, but here goes:
Before I had a child I had no idea how freaking hard it is to be a parent. None. At. All. On top of that, your SIL is a single mom. I can't even imagine. I have the support of family (occasionally), daycare, a babysitter (sometimes), and a very active husband who loves being a Papa.....and yet I feel overwhelmed and pushed to my limits more than I ever imagined I would be. I cannot even begin to imagine what a single mama must endure and the inner strength she must find to be a good parent let alone a good-enough parent. I assume she is working to help support herself and her son. Good on her! I agree that if her brother wants to and is able to help her out, not out of obligation but because he wants to (and it did sound a bit like maybe he doesn't want to but feels like he has to....maybe have a real heart-to-heart with him about this and find out), then you should try to find a compromise, as well as see the best in this.
First off you could and should set a limit and say you/your hubby only babysit every other week and make the other Saturday night your extra-special date night. See if your SIL can find a babysitter or another family member, or a friend to trade babysitting with or some other arrangement for the other Saturdays. Also, I would try to look at this as practice and getting a sneak preview of parenting. Not only the time spent with your nephew but learning to balance the needs of a marital relationship and the huge demands of a child. I did learn a lot from watching my friends who went before me raise their kids. I wish I had had more experience and time spent with children before I had my own. I might have felt better prepared. Because I can tell you, and there's no way you'll know until you're there: but being a parent is really intense. Maybe spending the time with your nephew will give you a glimpse so you won't be as shocked as I was to discover just how hard it can be.
And if all else fails, and your hubby really wants to help his sister and isn't just doing it out of a grudging obligation, then just make Saturday night your girls night or your night for yourself and enjoy that, and find time somewhere else to connect with your hubby. BTW that is another skill you'll need once you become parents so might as well practice now. Oh and I forgot to mention, once you have a kid this will be time banked and your SIL will probably feel more interested in helping you guys out (which you will need!)
Best of luck to you. Your feelings and needs are legitimate and I hope you can find a balanced solution.