I've fix a lot of loose sights by using a shim made from a piece of discarded hacksaw blade.
Heat the blade first to get rid of it's temper so you can work with it easier.
I make the shim to fit one of the sides of the dovetail,,not onto the bottom of the dovetail base.
If you put a piece onto the bottom of the dovetail base, it pushes the entire sight upwards. If it's quite loose to begin with, it can look kind of odd with the leaf sitting far up and off of the surface of the bbl flat.
If you're working with a rear sight style that doesn't have a leaf extending back, or a flat portion that needs to sit flat onto the bbl, it's really not an issue however.
The tiny shim to fit the side of the dove tail is filed out but not cut off of the hack saw blade, Makes handleing it easier.
Clean up the bbl dovetail (both sides) for a fresh start and then trim till the sight base along the shim can be barely knocked into position on the bbl.
You'll have an easier time pushing the sight in from one side and holding the shim in from the other as the long 'handle' of the hacksaw blade won't be in the way.
When it ready to go,,soft solder tin the shim and sight base contact surfaces.
Use a soft lead pencil (graphite) to coat the surfaces on the shim, the sight and especially the bbl dovetail itself that you don't want solder to stick to.
A tiny touch of flux to the surfaces to be joined,,,hammer them into position in the bbl dovetail itself.
When your satisfied that the shim is positioned right and it should only go in one way if it's tight,,sweat solder the two pieces together right on the bbl.
The pencil graphite will keep the assembly from soldering itself to the bbl and solder from creeping up onto the sight itself.
When it's cooled off. Tap it back out of the dovetail, cut the excess shim off and file to contour.
Cold blue or brown to match. Clean up any residue on the bbl surface and reinstall the sight.
That's pretty much a permanent fix to the problem. I've seen many fixed using the same idea but the shim is just driven in along with the sight and trimmed off. Nothing soldered. That'll usually hold too, but will move with windage sight adjustments and may not return with the sight if it's wacked in the other direction. Many are crude repairs to say the least, done after the obligatory hammering of the dovetail edges and usually some burrs turned up in of the bottom of the dovetail.
If the dovetail is just totally trashed and oversized, the entire area can be cut out squarely and a new piece soft soldered in place. The new tight fitting dovetail then cut in that piece. The newly inlaided piece does not have to be overly large, just enough to remove the damage. The rear sight often covers solder joints from above and the any joint on the sides are up high enough so as not to be so noticable around the sight. 50/50 or 60/40 lead solder will darken with age anyway and a nice tight sweat solder fit will help matters from the start.
