I have looked at your .ai file thinking it was something with stroke scaling, but the problem is actually that you have too much details in that area to scale it properly at such a small size.
The full height of the part on top of the helmet is 23px. If you try to reduce it to 10%, it only leaves 2.3 pixels for that part. It looks bolder because you get an average color between the black of the shapes, their darker beige fill and the yellow-beige of the helmet, which "clogs" the space and makes it looks bolder.
At 50%, you can still see details:
At 30%, you can see that it's starting to "clog":
At 10% as you're doing it, the whole area is basically filled with dark grey:
However, if I delete some of the details within this area like this:
Then the area remains open. You can also see that you have only 1 or 2 pixels between the top and bottom of that area:
Which gives a better result:
It will be up to you to determine what detail you want to keep to scale it basically to the size of a postage stamp.