Do I Need New Carbs?

I don't know much about old British bikes but I wouldn't have thought worn carbs would cause vibration. Is it because he couldn't balance them? Service them yourself

 

I guess it's possible the carbs could cause your problem but unlikely IMO. A partial jet blockage or other fuelling problem in one carb could give rough running in the relevant cylinder but simply being out of balance usually affects tickover and has less effect the further you open throttles. Either way a carb service/rebuild to replace any worn parts should make them as good as new.