Great idea. I never thought of weighing the brush.TLDR: My preferred break-in process is through continued use with accelerated drying.
I recently acquired a Zenith unbleached boar and today I used it for the first time. There was no special break-in ritual. I took it out of the box, soaked the bristles in a cup of water (cold tap) while getting ready for the day, thoroughly rinsed and gently squeezed out most of the water, and took it to the puck.
After the shave, I placed it in front of a fan (an electric fan should be standard issue in Texas) so the bristles would be dry before tomorrow's shave. I happen to agree with the "You want the brush completely dry to encourage the split ends to happen as quick as possible." statement from @GoodShave (and others) and wanted to accelerate the drying time. I weighed the brush when it first arrived so I already knew the dry weight. After less than 8 hours in front of the fan, it was back to its original weight and ready for tomorrow.
Reminds me of what my wife told me. She told me to go on a diet and get back to my original weight. 8lbs. 13 ozs. Hmmmm.