Belts not intended for carry will stretch. I had a reasonably thick casual belt that stretched after a few months carrying.
Gun belts are thicker leather. Some are even made with stiffeners to help resist stretching.
An actual dress belt doesn't stand a chance with anything bigger than a back-up gun, I would think.
And, if you're gonna carry a 629 at better than (40 oz?), you're definitely gonna need a belt made for carrying a gun. That or towing hitch--those 629's are heavy. I'm betting the only thing heavier is a Redhawk, not counting the X-frames. Even if there are a few guns heavier, a 629 is a lot closer to the top of the weight scale than the bottom.
If budget is an issue, take your time looking around. I bought a gun belt five or six years ago. Black, very plain. No-name brand. It hasn't stretched with almost daily carry. Its one attribute is that it is rather thick. Cost was $25.