It's 94 integra gsr, driver's side low beam weak, has 11volts and high beams dead. Passenger's side bright on both low and high beams with a little over 12 volts. Is there a relay that controls the driver's side headlights?

Are you using factory head light's / bulb's
What do your grounds look like? Hondas are known for poor ground's on the head light circuit (worse if you tried to put larger bulb's in).
Just because you have power doesn't mean you have groind and you need bolth for the circuit to work.