The asp.net is base on pools and not on users.
Some memory per user is going on user session, but I believe that you not hold huge amount of data on sessions (did you ?).
Now I suggest ti run process explorer from sysinternals, and check on w3wp.exe the working set and the virtual size of the memory for this. You can do that by open this 2 columns on Process Memory tab.
Then you see there how many memory asp.net needs for your application.
Second step if to check how you have configure your pool by open it. Maybe you have configure it to recycle too often, or to recycle when you have more than 125k working set memory, and your program have 200k working set memory. So you need to recalibrate some values.
Together with process explorer you can see how much memory your application need, and setup correctly the pool.
Of cource maybe there are other problems and other issues with the memory but asp.net is not eat memory for every user and you need to check where your memory is used - and the process explorer is a good tool for this job.
Hope this help.