Both the Weatherby and the Browning seem good rifles. My own preference would be the Browning, but really it will come down to which one you prefer the feel and features on.

On the A-Bolts, my own has been used in dusty conditions - spent days covered in fine red dust in fact. It has had times when it has been out in rain for a solid week at a time too. Nearly 20 years of use, and truckloads of game, but yet I've never had a problem with the trigger, or any other problems with function. I don't baby it either.