You can forget about the earths for the moment. If a short is blowing the fuse then the problem's in the live side: probably insulation worn through and intermittently touching some point on the chassis.
Another possibility is too much load. Do you have higher wattage bulbs in the headlights or has the right hand unit been modified so both filaments are on together, for example?
However my top candidate for the cause of your problem would be be the fuseholder itself. Are the contacts clean and gripping the fuse firmly? A slightly high contact resistance in a circuit supplying a dozen amps or so can easily result in a few watts being lost in the holder... it's not designed to dissipate heat so the temperature can get high enough to melt the plastic.
If the fuseholder's still useable then disconnect the battery. You can then take the female connectors out from the holder by pushing a very small screwdriver (or one of those big staples they use to hold cardboard boxes together straightened out as a cheap alternative) in to release the tang... it'll then pull out the back. Clean up the connector, give it a gentle squeeze with a pair of pliers to tighten up the contact, bend the tang out a bit so it clips back into the fuseholder socket securely.
