When you say you're chasing yourself around the target, it made me think you may have a possible parallax issue with that old Weaver, too. Does the rifle group o.k., or are you just taking a shot, and then making an adjustment? Do the X-hairs hold exactly center on the target if you move your head and eye a bit left/right and up and down?
If you haven't yet, try this the next time you shoot; it's very easy to do and costs you nothing but a few seconds of time:
Dead-rest your rifle with the X-hairs centered on the bull @ 100 yards. Then, without touching the rifle, look through your scope and move your head and eye around and see if the X-hairs stay centered on the bull. Sometimes the center of those X-hairs chase all around the bull except in the center. If that's the case, you've got a parallax problem. When I mount any scope on any of my rifles, that's the first little test I do to make sure I don't have a parallax issue. If your gun is grouping o.k., then your probably all right, and that's one less thing. From time to time when I'm shooting, and if I think of it, I'll just quickly do that little test just to check for any parallax gremlins. Leupold scopes, at least the ones I have, are gremlin-free.