The only two problems with larger tires would be clearance and rolling resistance, other than that they simply provide greater traction (contact patch) and some small shock absorption when hitting road irregularities, protecting your rim and helping to prevent "pinch flats" at the greater speeds of motorized bicycle riding.
Just about any name brand bicycle tire is made well enough that you wont experience any "shaking" - even as inexpensive a tire as a $15 Kenda. I did have some problems with some generic "industrial delivery" tires, often used on rental beach cruisers - but that wasn't a surprise, they were obviously "lumpy" and cost a whopping $6 each lol
I happy run 2.125 tires on all of my MBs save my old dutch commuter, which simply has no clearance for such... would if I could tho