Heavier bullets usually hit a target higher because they recoil more and are slower...This means they are in the barrel longer and the barrel jumping up (recoil) sends them higher...Doesn't make sense to some but that's the way it is...You see this especially in handguns and muzzleloaders...

Now, to your other problems...I bought a Ruger M-77 in 1980, still have it...Now, mine is in .243 but I've done a little work to mine to make it shoot better...First, before I took it home I had the gunsmith adjust the factory trigger to 2 1/2 pounds...

Second, and this happened 20 years later as my gun shot well for years...The barrel on those guns are not free floated, they come with pressure on the barrel...Now, I have helped some rifles by increasing this pressure...Take a shotgun shell, cut a 3/4 inch section out of the middle, then cut this in half and slide it between the barrel and upper forend...Adding pressure gives you a stiffer barrel and this could fix your problem...

Now while we are on this...You are certain your scope is OK??? This is crucial...Also, with that gun you can check all the scope screws so make sure they are tight...Finally, turn the gun over, there are 3 screws...Two for the trigger guard and the tang of the barrel and one under the floor plate...To tighten these screws start with the larger one under the floor plate, tighten the heck out of that one...The other two, make sure they are snug but don't over tighten...Changing the tightness of these screws will change bullet impact...

So far, everything I've mentioned is free, so they are the easiest to do...You might even want to put another scope from another rifle just to make sure your scope is good...

Finally, I did end up shooting my barrel out about 10 years ago and I was losing accuracy...I considered rebarreling to a 7mm-08 but I had a bunch of .243 ammo so I had it rebarreled and free floated and pillar bedded at that time...