You have quite a bit of variation in the recorded weights.
Would it be possible to work with the supplier of these parts to reduce and understand the causes of the weight variation? I would look at trying to work with the supplier in the first instance.
Are they aware of the critical nature (to you) in this process?
Once you understand the root cause of the variation it might be easier to work on some solutions to eradicate the variation (never completely, but at least improve it).
Then repeat the study, or get the supplier to put some in process checks in place to detect the weight changes etc.