As the putter is allow, I doubt it doesn't already use a helicoil (its a steel thread insert put into holes in allow to create a thread as alloy is generally too soft for a steel or stainless steel screw to bite and hold).If you’re confident in DIY, easy outs are good for the removal. My only concern would be if the screw was tight enough to break (potentially rusted) you risk snapping the easy out in the thread that’s left too and then the putter is knackered.
You may be better speaking to a local engineering workshop, but they always suggest helicoil but that will effect the weighting Albeit on a small margin.
As the putter is allow, I doubt it doesn't already use a helicoil (its a steel thread insert put into holes in allow to create a thread as alloy is generally too soft for a steel or stainless steel screw to bite and hold).
If they had any sense at the manufacturing, I imagine the screws (if they are supposed to be removable) would be stainless steel)
I would try a screw/bolt removal attachment for a drill driver, alternatively carefully drill the bolt out. If ppush comes to shove and you mess the hole up, you could araldite a new weight back in place after its been prettied up