I think that part of the issue is that the Berger bullets are a secant style, and the accubonds are a tangent. It plays with the distance that the different bullets styles have to jump to the lands. I shoot the Hornady A-max and Nosler Accubonds out of my 7mm (a remington), and have matched their velocities appropriately to have their trajectory's match. I had to play around a bit with the OAL as well as the powder charge for getting the velocities that I wanted, and I ended up with a smaller powder charge and shorter OAL on the Accubond load, and a longer, larger charged load with the a-max. I did load some rounds with the Accubond that were the same length and powder charge as the A max, and after firing one had to put them to the side and pull them apart when I got home. Way too hot. It was that the bullet was too close to the lands with too large of a charge. I haven't loaded for a weatherby, but i would just start with the standard OAL and charge, and then find what seating depth works best for accuracy for each bullet. I would then up the powder charge for each load until you get the velocity that it should be going at. You might have a smaller charge, but you are running at the same pressure because of the bullet being closer to the lands, and jumping the pressure up sooner.
I wouldn't recommend changing bullets in a given load from a secant style to a tangent style just because of the tangent bullet contacting the lands sooner, creating higher pressures, and thereby more velocity. The problem is that you would be over pressure. A lot of rifles might not even show "signs" of high pressure. If it is made very well, and true to itself, you won't experience a sticky bolt. If you have a tighter chamber, you might have zero brass flowing. But you would still be over pressure. Most rifles can handle it just fine, since they are proofed to much higher levels, but it is still risky. What if you're using that too hot load, on a warm day, and are sitting in the sun with your rifle out? That might turn out some problems if you shoot.