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