The displacement would just be too high. Even IF you could make it work, spinning a weed eater engine pump with a weed eater engine at 8000 rpm would result in around a 50 gpm water flow. 50 gpm water flow would require over 100 hp electric motor or almost 200 hp gas engine to achieve 3000 psi for pressure washing. Plus you'd never be able to hang onto it, the weed eater engine pump would disintegrate, etc. There's really just no way to make it work at all.
If you look a triplex pressure pumps (what a good power washer uses) they have 3 cylinders to minimize pulsation, ceramic plungers, very small bores and strokes, multiple high and low pressure seals, etc.
I have a Cat 820 triplex pump with an 18 hp engine and it does 10gpm at 1000 psi. It's not good for normal pressure washing, but it's awesome for blasting caked mud off trucks and equipment, and large washdown jobs.
If you want to build a pressure washer, go on eBay and look for a small CAT pump like a 3cp series and pair it with a gas engine. The pumps are fully rebuildable and will last many lifetimes if taken care of. I am partial to cat pumps, but General pump, Hypro, AR, and Comet are all similar design and equally good.
Cat pump manuals and parts lists are all available on their website, and the manuals include RPM and HP charts for calculating how big a motor or engine you need.