Pens vary in weight. Typically between 8g to 16g .
Here are a few examples of pen weight:
Wacom Pro Pen 2 (KP-504E) 15g
Huion PW600 15g
XP-Pen X3 Pro 10g
If you want to see more pen weight data see: Pen weight comparison
The vast majority of EMR pens are not designed to have their weight altered.
The only exception to this is the Wacom Pro Pen 3 which can be easily unscrewed and a custom metal rod from Wacom can be inserted to add weight to the pen.
If you do want to add weight to the pen, consider adding tape. Many osu! players add raquetball tape aorund their pens for a bettwe grip. Maybe that would add enough weight for your needs.