Will Fat Injections in Marionette Lines Reabsorb? I Don't Like The Results.

You're right that the take of fat is less in more mobile areas of the face such as the mouth. This doesn't mean that it will all resorb necessarily. I would expect there to be swelling in the area at only 6 weeks from your procedure.

Steroid is a consideration to help though I would suggest you talk with your surgeon to get a better sense of what to expect and whether waiting at first is best.

I dont see the final results after fat transplantation to the face until about 3-4 months after surgery, so be patient.  Massage may help, but more than likely it will improve on its own without steroid injections.  Fat is typically injected deep below the skin level so risks of bulging and irregularities is lower than injectable fillers such as Restylane.  Swelling stays around for quite some time with fat and patience is key. Good luck!

I think your final results are likely not yet apparent at 6 weeks. You likely still have some overcorrection and edema distorting your result. Give it another 4 months or so before you consider any revision, as long as your operating surgeon seems to think things are going within normal limits.