At my first post op implant appt. my doc removed my plastic "disk". He popped it off with him fingernail, it sailed across the floor, he picked it up and threw it in the trash. Said I didn't need it anymore.
However, I know lots of people on the Cochlear Community (a discussion forum similar to this one) who wore their disk throughout the healing process and were even told to keep it to wear after they were healed.
This is one of the many areas where docs differ with their "rules" - and personally I'd follow what your doc tells you whether you agree with him or not. Afterall, he's the doctor
As you say, the disk is pretty weightless, so it won't "pull" on the abutment and rod. Taking it on and off - because it doesn't have any real weight to it - shouldn't interrupt the osteointegration. My doc told me wearing the processor before the site was fully healed/integrated was an issue because of the weight of the processor. In his words, wearing it prematurely would cause "torque" and could very possibly lead to the implant not remaining where it was supposed to be.
Hope this helps,