Is it unreasonable to set assignment deadlines on Saturday/Sunday?
Don't assume anything about your  students' schedules. Set your deadlines so everyone can manage their time based on their own needs.

You are concerned about encouraging your students to do work on the weekends. Consider that many students have customer service jobs that require them to work on the weekends (retail, restaurants, etc). They might work nights or swing shifts. They might have children to care for at certain times. You have no way of knowing if doing homework on a Saturday or Sunday is convenient for them or not. 

Don't arbitrarily pick a deadline based on what you perceive to be best for them. Give your students a full week to work on assignments if you can, because they might only have small chunks of time available to do homework. Make it due when it really needs to be done, such as when the next class starts.

For example, I worked 10 PM to 7 AM Thursday through Sunday for my first couple of years in college. I often worked on homework during my lunch breaks, which could be at 2 AM on Monday morning. I'm sure all of my instructors assumed I would/should be sleeping at 2 AM, but it was actually a perfect opportunity to finish up homework. 

Since there will always be students that procrastinate, and some percentage will inevitably have an emergency at the last moment, you may want to make it clear at the beginning of the course that you are not able to grant any extensions for any reason, because the deadline is already at the last possible moment. Also give the reason why that's the case, whether it's because you will review it in class, or there will be a quiz on it they need to be prepared for, or whatever the reason is. Be clear that since you are already giving extra time, you expect them to manage that time properly, so that an unexpected difficulty does not make their homework late. 

You can always choose to make exceptions later for truly exceptional circumstances, but having a clear policy that you don't make exceptions will discourage people from taking advantage of your already generous deadlines. I've taken many classes with this policy, and I've never heard anyone complain about it.