Oh, right, it has something to do with the line attached to pivot point? Thank you, that fixed the issue!
(And sorry, seems like this solution has been presented multiple times, just didn't realize it would solve my issue, too.)
I expected that the sprite would scale on one axis only, but it seems to stretch the sprite on multiple axes very unintuitively. Also the child objects don't seem to scale correctly with the parent. What am I doing wrong? Here's some screenshots that might explain a bit better: