Tightening your sites won't help the peep.
Get a new sight cover and another sight aperture or two. By trying different apertures you can find one that fits more snug.
You can also get a NM aperture and stone it down til' it fits just right.
a cheap-o fix for temp is to take a rubberband and have it go around the aperture and your windage knob. Just a temp fix mind you.
There is another method of tightening the sight base that I've used on a Garand or two, but it's kind of advanced.
Lots of options