Check and see if it is pressure bedded up in the forend. Its usually just a hump down in the barrel channel of the stock meant to put upward pressure on the barrel about 2 inches back from the end of the forend. If it is pressure bedded, you can always remove it and free float the barrel and see if that helps. If not, you can build the hump back. Another way to look at it is...The first two shots are right there and it's a 340 so if your doing your part, the animal is on the ground before shot #3.
Some other things you can play with is action screw torque. I think weatherby suggests 55 to 60 INCH pounds of torque. Some people like to play with that by starting at 30 in lbs and working their way up in 5 in lb increments to find the sweet spot for accuracy. Of course you'll want to check for normal stock culprits like the barrel channel pushing on one side of the barrel or the other. Check that the action sits flat in stock and bottoms out and doesn't rock back and forth. This would cause the action to be binding when the action screws are tight and would affect accuracy. I'm pretty basic. I'm sure there are alot more shooters on this forum with alot more suggestions on your problem. Good luck. Another reason to get out and shoot. You can always send it back to weatherby also. I think they have a 1.5 in guarantee. For what it's worth.

At 100 yards, my first two shots are right where I want. I have it sighted in at three inches high at 100 yards so by aiming at center the first two shots were three inches high and centered. The remaining shots after that will range within a eight to ten inch circle. Most have been high. I also shoot loaded up 45-70's and I don't have any trouble with flinching. Normally I shoot in three shot groups and then let the barrel cool. I took the rifle to a gunsmith today and he is going to glass bed the barrel and make sure it is free floating. He thinks this will take care of the problem. I will report back! Thanks! P.S. I also have a brake on this rifle and recoil is about like a 270.