Weld

If the weld is mostly lying on the surface, then yes. If the joint was prepped to include some gap, then probably not much.
If I jam two pieces together and just run a bead down the butt and then flush grind it, those kind of welds break a lot. Lots of times I'll jam the pieces together and tack them, then run the edge of an angle grinder wheel down the crack to open it up so the weld can penetrate. Depends.
Grant

I don't know if it weakens the weld, but it does reduce the cross sectional area of the filler metal that is actually the "patch". I do know that for bend testing, failure can result if the tiny grooves are running across the bend in the wrong direction.
Steve

An excesive buildup (>~1/16-1/8") of weld metal above the surface of a 'full penetration' weld wil make the weld more ridgid than the base metal, and this combined with the stresses caused by the weld shrinkage and the normally greater strength of the weld deposit can cause a concentration of stress in the edge of the fusion zone and can lead to cracking beside the weld.
This is similar to failures caused by repairs that have been 'reinforcd' by 'fish plates' which also tend to concentrate stresses in the area adjacent to the now more rigid repair zone. There are several techniques used to attempt to distribute the stress of the weld on the base plate and to reduce the concentration of stress adjacent to a welded repair. These techniques were more commonly required on older poorly designed digging booms which cracked much more frequently than modern designs.
I do know that for Grinding marks can cause stress raisers or notches that can lead to failures especially in high cycle loadings.
Just my .02