If I understand,
View -> On-Screen View Options -> True Line Weight.
As for printing, all output is true weight unless you choose 'Hairline' in the print dialog. The On-screen options are on-screen only, and not saved with views.
Check your pen sets as well. Perhaps you have a set active where the weight of that pen isn't what you expect. Printing from a model window, the print will use the model's pen set. Printing a layout, the drawing could have the model's pens, the layout's, or an assigned pen set. HTH,