You didn't show what model your talking about. Click on whichever product you're talking about, then go to questions and answers, and then click ask the community. That'll show us Wich model you mean. But if the barrels made for 223 Remington, then no do not shoot 5.56 out of it. You can shoot 223 out of a 5.56 but never vise versa. Hope this helps.

if it is a 223 chambered barrel you should not shoot 5.56 ammo through it the 5.56 ammo is hotter and could cause issues

Rickey, no Weatherby Rifle specified but, for warranty and safety reasons, I highly recommend asking Weatherby Customer Service at 307.675.7840 Monday-Friday
8am-5pm MST

Rickey, no Weatherby visible. Try again with model and/or upc code.