What type of upper body weight exercise can i do after finger fracture?

Depends: If you are still healing your fracture, it will be difficult to do upper body strengthening. You can wear weighted wrist bands and do some strengthening that way. However, free weights that require gripping are usually not possible. Nautilus-type machines where you can rest the bars on your wrist may also be possible. Once your fracture has healed, you can resume your normal lifting activities.