Can my chain of command stop or mess up my MEB?

*process

There's nothing wrong with the CSM asking your leadership where you are at in the process.

Why would a CSM try to stop someone's MEB? Your CSM can't stop a MEB but I don't see how it would benefit him to stop it.

The entire NCO Support Channel and Chain of Command should be tracking your MEB. He is likely asking just so he knows your status. Remember that the CSM is responsible for your health and welfare, and is also responsible for making sure you get the proper care AND the proper training within your medical limits. It is incumbent upon him to know what your status is, as well as your limitations. And... when the time comes, he is also responsible for making sure you get out of the Army without a hitch AND replaces you in a timely manner.

Don't read into it. CSM is just doing his job.

Your CSM is simply tracking your progress, he and the BN Cdr. receive weekly updates during staff call, the fact that he is inquiring is a positive thing. Whether he is encouraging/coaching your COC, or simply thinks you are worth the extra effort. Stop an MEB, not at all, there is only negative effect that would come from a COC trying to influence the process.