I have not heard from any patients yet with increased muscle weakness from these medications, so you may want to call the patient assistance line for Ilaris 1-877-452-7471 to ask about this, and talk to your doctor too.
There are patients that have had issues with lax muscles, or tendons in some cases of CAPS, which can be present throughout the body, but this has been noted more with patients that have more chronic inflammation, and were noted before going onto medications for CAPS. This can persist to some degree while on medications, but for some it improved.
We also have a large CAPS community on facebook in a private group with almost 200 members http://www.facebook.com/groups/41019328476/ it is private, but you can ask to join. I will ask the group this question and get back to you, but feel free to join and ask too, or ask on the rarediseasecommunities.org CAPS group too.