However, when I also specify the number of desired points of the scale, the buttons get wider/ narrower when specifying different anchorwidths...
This will only happen if you try to cram more buttons on the screen than your screen can accommodate *and* specifiying a very small anchorwidth. E.g.:
<likert ratingquestion>
/ anchors=[1="nice"; 10="meh"; 21="yuck"]
/ position=(50, 90)
/ anchorwidth = 3%
/ numpoints = 21
</likert>

vs.
<likert ratingquestion>
/ anchors=[1="nice"; 10="meh"; 21="yuck"]
/ position=(50, 90)
/ anchorwidth = 4%
/ numpoints = 21
</likert>

Basically, the distance between buttons can't be adjusted below a certain minimum. However, if you require that many response options, <likert> elements may not be the best option anyway. A <slider> may well be preferable. And if all else fails, you can always build a custom likert scale as per https://www.millisecond.com/download/library/v2/CustomLikert/customlikert.zip.