STOP, Before you shim or reverse ring, First take it off, completely, What rings? If Leupold: using a wooden dowel 1 inch (1 Inch scope??) turn the front ring to aline the dowel with the bore,' (Assuming you don't have a leupold ring wrench??) Now set the rear ring loosely in the rear base. (If using weaver style, set both finger tight only) Lay the dowel in the ring bottoms (top removed) and spin if, does it spin freely and cleanly? now set the scope in and tighten (do not "monkey torque" the scope ring bolts)
now remove the bolt and look down the bore at a SPOT on the wall, or a paper target 25 yds away (or across the room) start tightening the bases alternately until they stop, checking the alingment of the bases. Aline the cross hairs with the top of the bullseye or mark on the wall (Electrical tape works great !!) At 25 yds (+/-) the cross hairs should be about 1 inch high. Using a laser boresighter, the "spot" should be about 1" low. Check the torque, Here, I suggest loctite on bases only not on ring screws,
For shiming, take it to a gun smith with the proper shims, or make sure you have the correct bases.
It's been a while but I saw a similiar problem, I believe, If I recall correctly, the Remington 700 bases has the same hole spacing but the rear is thinner or not as tall as the Weatherby.