I ran into this problem today.
First of all, I will share with you the most common issue that should clear up your stroke issues.
Then we will look at another possible cause.
Go to Edit > Preferences > General >
Click the box next to: Scale Strokes & Effects
Did that clear it up?
Usually it will, but if you are like me and have always known that and it still didn’t work, try this:
Go to Window > Transform >
Unclick the box next to: Align to Pixel Grid
That should work.
If it doesn’t try expanding your object by going to:
Object > Expand
Object > Expand Appearance
You wont be able to edit the paths any more but you should be able to scale it.
If that doesn’t fix it comment below and we can see if we can find a way to help you out.