It can be hard to see the problem when you don't give all parts. I have not had any problems combining all parts. As @CardinalSims says, it appears that your "eyes" are under weight. I noted that headnew holds no weight.

@CardinalSims, replacing thru the edit section can be useful. Prior to having MS, I replaced parts that are muti group, but a single .wso in that section. Also, when I make height altering boots, I replace the bonedeltas as .bin, to match my boot height.

You know, I just remembered having done this... Instead of using headnew bone, for a mask, paint as hat grip. I would start by painting the area that is usually headnew, at around .200 strength, and see how that works in game. That includes the part you call "eyes". You can also paint the whole mask, except the last rows of faces, so they match up to the neck.

Good to know!
I'd never seen that mentioned before so I wasn't sure if it was something experimental OP was trying or if everything would be intact in that format

I tried normalize all for all the vertex group but I get the same issue. I can't convert the geom to wso since I get an instance error. Importing as bin is the only way the bones and weights are preserved, at least for me.

I guess you can say this is an experiment. If this works out, I will plan on making more of this type of cc.

@LadySmoks I will try painting to hat grip. Do you get the same problem when testing it in cas? I isolated the problem to the eyes, because it still happens without the mask part equipped.

I don't know anyone else who replaces via edit project contents either. I'm sure someone does it. It was something I tried out of desperation, since I didn't have MS at the time, and was replacing meshes in a multi group that imports as a single .wso. It says, geom, but you import a .wso to replace them. Then, more experimenting, and found that I could replace the BONDs, which are .bin. Convenient for height altering shoes/ boots. I now keep a file of both S3PE BONDs and .bin for TSRW, from +1 unit thru +11 units.

@makiura, what hat grip does, is allows you to use the hat sliders on the mask, which is separate from other head/facial sliders. Do NOT paint it to 100%, since then you lose the other sliders. As I said, start at .200 and see how it works... then make adjustments to paint levels.

I didn't test in game. I looked at your bones. It looks as you transferred the entire face to the eyes, then deleted bones you didn't want??? If so, you can't do that. Each vertices must be weighted. There are several youtue tutorials on bone painting.

In the case of underweighting, Normalize can't fix this if there aren't at least two groups assigned to the same vertex to average the weights from.
ie. if a vertex has just one group with 0.5 weight applied, it will stay underweighted at 0.5 - if you add another group with a weight of 0.2 for that same vertex, Normalize All will decide how to increase or decrease their relative strengths to equal 1.

To make sure that Normalize has at least two weights to average, start by assigning a group to the entire mesh before adding your own weights.
In this case, you'd assign HeadNew with a weight of 1.

I'd then add my next group and lock it- so that Normalize All will subtract what I painted from HeadNew rather than averaging them. To keep the weights predictable, I add the groups one at a time and repeat the lock + normalize + unlock each time. (Not manually, Lock Active handles that, but it makes more sense to describe how it works this way.)
Use Limit Total from the Weights menu as your final step, and you should be good to go.

I followed both of your instructions, and I believe it's working! I'm officially done with this. This project pushed me way out of my comfort zone, but I'm so grateful for your (@CardinalSims)'s guidance. Thank you for your patience; I struggled with a lot of the steps at first, but now I have a much better understanding of blender weights.