It is not practically feasible or convenient to replace only the bearing on these Seiko mov't. It is not even available as spare part.
The auto winding mov't must be checked on various points beside just the central weight being loose, which is kind of unlikely because if so it would have come completely off with time.
Bearing condition, that is how much free swinging there is. Something like the video below.
Shape of the magic lever tips, if worn it must be replaced - which requires disassembly main bridge.
Condition of the knurled wheel where said tips bite. It supposed to be lubricated but that is most often neglected by both factory and "watch repairers"
Orientation of the weight when reinstalled, to get max efficiency. In theory that should be reversed when watch is worn on right arm.
What I suggest to the OP is that he only gets the watch correctly regulated on the timegrapher by an budget watch shop. Anything else is likely to exceed the cost of a new same watch, which is about USD 60.