I think I've got a solution that will help lessen the burden (on both you and your students), make it part of the weekly schedule, and make it meaningful. I actually
My teaching partner and I would look at the concepts that were being taught in the upcoming week and create a homework assignment that supported that content in some way. We always changed up the format. It may have been vocabulary practice or usage, short content related reading passage with 5 questions, calculations, labeling diagrams, matching, etc. The bottom line is that the homework should take the average student no more than 15-20 minutes to complete and it always builds upon something they are learning about in class or something I feel that the students need more practice on in order to master.
Every Monday the students pick up the assignment as part of their daily handouts and they know that it is due by the last day of that school week (usually Friday). Of course, they are always highly encouraged to get the homework completed before the due date and hand it in, but for those with busy schedules (church, extra-curricular activities), a little extra flexibility is built in.
The DL Homework heading always looks the same (it has a distinctive box in the upper right-hand corner that says "DL Homework" and has the due date) so that there is no confusion. The students put the DL Homework in their yellow homework folder on the "To Do" side. I train my students early in the year to utilize any free time they have in class to work on this assignment. Most of them discover that they can easily complete the assignment in 2-3 days using only free time during their class. My only rule: It has to be done alone - no partners or groups. If I see that happening, I consider it cheating and I throw it away.
There was definitely a "learning curve" early on, but I was consistent in my expectations and within a few weeks, the majority of students were completing the work (ahead of time)! It is routine, it is predictable, and I started seeing results very early on.
Do you have a homework routine or a effective strategy that you'd be willing to share?