In order to dampen the stamina effect to something more realistic to prevent it from bobbing weapons into the 5th dimension, I've found these 5 simple steps seem to work very well for me.

1. Open the SharpeYe menu,

2. Click the "Details" tab,

3. Expand the "Alignment Meters" drop-down,

4. Select the number next to the slider marked "Run Speed reference" and set it to "500" (Note: If you have any mods that change player speed you can edit this value to match your sprint speed, ex: sprint speed=250, set this as 250, etc. GMod's default is 500),

5. Select the number next to the slider marked "Stamina Recovery" and set it to "9999",

Profit!