Dim Headlights. 2001 Jeep

Seems like an Earth problem for the RH lights.
Grab a Jumper lead. Attach one end to a good earth (engine or Neg. Battery post).
Other end to the RH metal mud guard.

your alternator or battery may be getting weak

Check the coil see if ur getting power to it

check for voltage at the battery with the engine running. You should see 14 plus volts. Now turn on the lights, bower motor, and whatever else you can to put the maximum draw on the battery. If the voltage drops below 13 volts the alternator is bad.

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i have the same problem on my 96 mustang. i even went bought new head lights and nothing

Check output alternator voltage at battery, with lights and a/c on, should have no less then 13 volts, if that checks good, check for bad ground at headlights, or find ground wire at headlight elec. plug (back of headlight), add wire to ground wire and bolt it to body ground.

The headlights on my Tahoe are dim too. It's also a 1999. I replaced my bulbs with Silverstar's but it was still dim. I used Mequiar's Headlight kit to polish off the yellowing and oxidized headlight's and it really made them look good but they are still not bright. They look bright but the light hitting the road is still weak. It's because the inside of my headlights are a little bit cloudy still. The heat damage from the bulb made the insides cloudy and the light is still weak on the road at night. That's all I can do unless I replace the headlight assemblies. Much money and not super simple to do. I have very bright bulbs just cloudy housings that still don't allow the beam to fully shine through. I don't know if that is your issue but I hope this helps.

TEST
remove both bulbs from the lamps but leave them on their wires switch on and see if the bulbs are still different brightness if not they the passenger side lamp housing has damaged mirror is dirty or missalined and needs adjustment. if they are different brightness then this may be a earthing problem.

Well you have a double ground somewhere. Check the the grounds for your headlights.

i had the same problem with my 92 cherokee laredo, could be the crank positioning sensor. if it goes bad you dont get spark from the coil. or it could be the coil, distributor, or even spark plugs.