Changing the bulbs to those that draw more amperage will do the same.
If this is the case, replacing the headlight switch will be only a temporary fix.
Hence, the reason relays are a good idea. (Even with "stock" illumination). Dan is absolutely right. Joe is clearly showing why you gotta make sure the stuff you have is in good condition also. It's why JUST putting in relays may solve your problem, but it won't FIX it.