There is no available method to change the thickness of that cursor, but you can change it to another cursor.
Open the old Control Panel (not the settings app).
At the top of the old Control Panel set View to large icons.
Open the Mouse applet.
Select the Pointers tab on the resulting utility.
In the resulting list, scroll down to find the 'Text Select' cursor.
Then click the Browse button and you will see a full list of the available cursors.
If you just need to make that cursor thicker, the beam)rm.cur may be a good choice.