Shot the boys maximums today with it's open sights. It was hitting 8" to the left. Last week it was dead on. The front sight is a dove tailed sight but no dove tail in the barrel. Instead its drilled and taped with one screw. It allows it to move when pushed. I had tightened it pretty well last week when I sighted it in. But it moved. I'm not going to mess with it i will just scope them. What's a desent scope that will hold zero and not be to large. I like 2-7x optics for hunting
Have you tried Locttite? I don't mean to hold the screw, I mean to hold the sight. I have a scope on an old Diana 35. Scope stop holes were inadequate - too shallow. I cleaned the dovetail grooves and applied Loctite. I installed the scope mount and let it sit for the recommended 24 hours. It no longer moves. If I ever choose to remove the mount I can clean out the Loctite. I'll then have the option of reinstalling the mount. You could try the same process between your rear sight and the barrel, just position the sight as desired then leave it set up.
While others MAY CRINGE on the BRAND, I have a $59 Barska 2-7x32AO Mildot that's pretty much in line with the more expensive Hawke Version I also own a couple of.