It sounds like your problem is that the printed media won't stick to the backing so when you weed it, the letters go a walking in all directions.
If this is the case, what you need is a stickier media along with a thinner overlaminate.
If durability is an issue, go with a sticky cast like 3M IJ170 for printing.
A sticky calendared like Arlon 4500 weeds well too.
For overlaminate, Arlon 3170 is a 1.3 mil cast for calendared vinyl and both Arlon and Avery have super thin, higher quality cast overlaminates. But pretty much any 2 mil cast overlaminate will do. I know 3M reps used to go apoplectic when you told them you used a different overlaminate on their precious material, but I've never noticed a difference.
We print and cut multi-colored logos and lettering regularly.