tl;dr: My best guess is that your process is fine and you aren't inducing preventable bias (unless the students are in competition with each other)
It may be that you cannot. It may be that your analysis is incorrect. It may be that a solution would be worse than the status quo. It may be that you need not make changes.
One solution would simply be to not improve this week's lesson but use the knowledge about the class to improve next week's lesson or worksheet and hold it fixed until the week following that one. Suboptimal, surely, but "fair" by some definition of "fair.
Your assumption that your sheets improve as you go is only your assumption. It may not, in fact, be accurate. Each of your groups is different and will interpret things in different ways. It may be that your improvement is a distraction or impediment to the next group (see below). It is hard to know until you interact with that group. Every student is different and all are different from you.
If you have thousands of students you can do a statistical analysis, of course, to determine if there is an bias effect.
You don't say whether your students are in some way in competition with each other (a generally poor practice). If they are, you need to worry about "bias", but if they are not then you just need to do the best thing you can for each student.
However, if you really suspect that bias is an issue and that some students are being advantaged and others disadvantaged by your scheme then you need to change, or at least adapt, it. You may need to set some time aside at the start of a lecture to get each group on the "same page" about the current state of things as you understand it. A few minutes of "warm up" at the start of the class can be helpful in any case. I often opened a lecture asking for questions that might have arisen, but you can also use it to make corrections/apologies/give encouragement/add emphasis...
A technical solution, of course, would be to provide some communication channel to all the students so that all can see any updated materials in a timely manner. You could even provide the lecture materials prior to the week's start and warn that they may be updated as the week progresses. Students could then, for example, print them out before class and use them to help follow the lecture. If you have a way to highlight changes to the base document, all the better.
I once taught the same course to three groups in back-to-back periods of about an hour each. I would take questions and use the questions from each group to improve the lecture for the following group so that the same questions needn't be asked. However, I learned (eventually) that the following group might not have the same questions and might have seen the concept clearly already, so I was proactively answering a question that needn't be asked or answered. This accumulated into the third section of course and I found it hard (impossible) to complete the lecture in the third section. Let each group be itself, but if you make a mistake, fix it of course. If you say something dumb early on, you don't need to repeat it to avoid "bias."
A follow up:
While I believe that you need to work to teach every student in every interaction (i.e. each class period for this discussion) it is probably beyond our ability to give each student precisely what he or she needs most at that time. If I am Socrates, teaching one student at a time, or if I'm an Oxford Don, teaching 5 student tutorials, I can probably do that, but with twenty to two-hundred students in front of me all I can hope to do is to make sure that each student can learn something that will advance their learning. Even that is a difficult task with mass education, but it can be achieved. Some students will learn more, because they are primed to do so, and some less, due to factors of their own making or otherwise. Teaching everyone precisely the same thing is not an achievable goal unless the everyones are just robots. Help every student advance. Don't favor anyone arbitrarily.