Thanks for your file!
I converted your document to use Pixels as the Units, rather than Inches.
I used the Transform Studio to make sure all your lines were 'pixel aligned'
I navigated to Preferences > User Interface and made sure 'Show Lines in Points' was unchecked.
I selected all the Curve objects and set their width to 2px.
With all the Curves selected, under Blend Ranges, I set Anti-aliasing to Force Off.
Now when viewing your document at 100%, all of the lines are displayed at the same width, do note when viewing at less than 100% zoom, Affinity uses Mipmaps to display the canvas, which may mean some lines appear thicker than others, but this will not be shown when exporting.
Please find a screen recording below showing these steps, alongside a copy of the edited file and my exported JPEG files after making these changes -
https://www.dropbox.com/s/h5lbw1wdyiuqdev/2021-10-15 16-05-41.mp4?dl=0
https://www.dropbox.com/sh/olajkjwmdbffhx0/AADoNPPYFarLbqxNI9Isj8F2a?dl=0
I hope this helps
Princess95 got a reaction from Dan C in Affinity Publisher - Lines weight changed after export as jpg