There are a number of Painting Cursor settings you can adjust by going to Adobe Photoshop Elements Editor > Preferences > Displays & Cursors:
Unfortunately, there is currently no thickness setting for the Painting Cursor. You might want to experiment with some of the alternative cursors to see if that helps in any way.
The Painting Cursor problem you are encountering is not specific to Photoshop Elements, with many Photoshop CC users also having the same issue. This problem appears to be getting more common as people upgrade their computers to ones with higher density screens. The latest update from Adobe is that they are aware of this issue and evaluating solutions. Hopefully, the Elements team will be able to implement a similar solution to the one that the Photoshop CC team finally decide on, at some point in the future.
There are some clunky workarounds mentioned in this thread that might be of use in the meantime: