I'd start by verifying you have the correct bases for your rifle.
Next question,what kind of rifle is it?Specifically,is it a sporterized milsurp or any other vintage rifle that may show tolerance variation at the rear bridge in particular.?(like stripper clip boss grinding).
Did you buy quality rings/mounts?Do they seem to sit down and fit line to line?
Really,putting on a scope seems so simple,and sometimes it is,but there are a lot of ways to get it wrong.
Bases tight on the rifleset the lower half of the rings on.No burrs,good clean fitup.Snug them up .Then set the scope tube in.Anything but a perfect drop in means lapping the rings.When you put the caps on ,use something,a dime,a credit card,etc as a gage to get the same gap between the upper and lower all around,then go around and tighten all the screws about 1/8 turn at a time till you just get some friction.Square up the reticle and set eye relief.Tighten like you were torquing a cylinder head.Not to crazy on the torque,its a thin aluminum tube.
Now,pull the bolt out.Sandbag the rifle.A buddy can help here.Look through the bore at an aiming point about 40 yds out.Have your buddy hold the bore on target while you twist knobs to get the crosshairs on target..
Use a bigger target,and shoot zero right on at 40 yds or so.You should be able to see your bullet holes in the scope.When you have that,back the target to 100 yds.
If you still have the problem,talk to your gunsmith.It may be you need your bases machined,or shimmed,etc.Likely you will need your rings lapped.Height problems translate to ring misalignment.Bending your scope tightening the rings is bad.
I don't use them,but some solve this problem with Burris Posi-line rings.They have eccentric sleeves that will solve your problem,likely.
You might check to see you do not have a sling swivel screw bearing on the barrel.