Homework - a lot or a little?

Today I did not check any homework because nothing was assigned the previous day. However, I did have a student explain that she would rather have me assign entire sections of the book instead of pieces of each section to focus on. My hope was that by having students focus on one or two key concepts, they would be able to complete quality work and critically think about their responses. What I told the student was that if she chose to she could complete the entire section if it works better for her in retaining information. This made me analyze and think about my current strategy I am using in my action research project because I know not every student is going to complete the entire section on their own if it is not assigned as a whole. Therefore, if I did assign the entire section, maybe I would see better assessment results from those individuals who do all assigned homework, small or big. But on the flip side, if I choose to have students complete an entire section, there may be a number of students who choose not to do any of it because it is just too much to complete.