The Weatherby's have from what I can tell a poor reputation for a couple of reasons. First, would be the "excessive" speed for bullets which in the past didn't hold up under close range shooting. With the advent of the A-Frames, TSX/TTSX, North Forks and any other high weight retention bullets, I'm not sure that this is continues to be a valid point. No doubt in my mind that with more frangible bullets at close range, the negative reputation was earned.
The second reason, would simply be because of shooters not being able to handle the higher recoil. This doesn't necessarily apply to you. But it wouldn't surprise me in days of yesteryear when Weatherby's were more of a gun for the well to do, that perhaps one too many hunters with more money than sense showed up at camp with his brand spanking new Weatherby thumper, because it was the best of course, with very little experience shooting it. And it showed during actual hunting.
As mentioned with the bullets available now, the Weatherby calibers finally now have a projectile worthy of the speed they generate. But in the end, you still have to adjust yourself to that extra bit of recoil in my opinion.
I think Phil pretty much summed it up here, and I lean more to his second reason.
Before the introduction of Vanguards and composite stocks, the Mark Vs were mostly more expensive, fancy rifles -- something that not a lot of average American hunters had.
I've taken my .375 RUM on two trips to Africa, one shooting 300 grain TSX bullet and the other with 270 gr TSX bullets, with both loads about 200 fps faster than the same bullets in a .375 Weatherby. These bullets performed extremely well on shots from 30 to 348 yards, and on all animals from Steenboks to Buffalo and Eland.
They are push feed guns and most people on here are control feed guys. Nothing wrong with them, I guess I like standard calibers too. Easier to get cheap ammo, if there is such a thing anymore.
I hunted for about 40 years, taking scores of North American animals and went on two African hunts, which included a Cape Buffalo hunt, before I got my first computer and learned the difference between push feed and controlled feed rifles, even though two of my small caliber rifles were control feed.
Weatherby factory loaded ammunition has always been more expensive and not as available as ammo for the "standard" cartridges, including the 7mm Rem mag and .300 Win mag. Ever since I got my first centerfire rifle, a .30-06 back in 1967, I have only shot handloaded ammunition. With the same bullets, and not counting the cost of the cases, it only costs me about 10 cents per round more (for the additional powder) to load for my .300 Weatherby than it does to load a .30-06 cartridge.
... The only reason I will hesitate to take it to Africa when the time comes is that it has a muzzle break, and if the PH is uncomfortable with that then I will leave it home...
Like I posted above, I've taken my .375 RUM on two African hunts, and I took my .300 Weatherby on another African hunt and on a New Zealand hunt. Both of these rifles have KDF muzzle brakes on them. With the variety of game species that I wanted to hunt on these trips, I hunted with 8 different PHs in Africa, and 2 different guides on my New Zealand hunt. None of them ever said anything against the muzzle brakes. My New Zealand outfitter also had a variety of rifles available for hunters to use, including at least two with muzzle brakes.
Watch the African hunting shows on the outdoor channels. Many of the client hunters shoot rifles with muzzle brakes. I have also seen quite a few PHs on these shows that wear ear muffs, and a number of other PHs and trackers that will hold their fingers over their ears prior to the clients shots -- regardless if the client's rifle has a brake or not. I take extra foam earplugs that I give to my PHs/guides, and I'll tell them to hold their ears before I shoot.