Definitely a short (unless you have the wrong size fuse in there). i would check the bulb sockets and make sure nothing is in them like metal pieces, shavings or water. I would also make sure they aren't loose. and make sure whatever insulates the socket from the contacts is intact.
Check the switch for the headlights, make sure it isn't broken, cracked or wet inside.
If it happens when you turn on the marker lights but not the headlights you will reduce the number of wires you need to check. And wires are the next thing you need to check. The main places are anywhere they connect to a fixture or connector body and anywhere they pass through a body panel.
You are looking for loose connections, frayed connections and places where the insulation is worn from rubbing against any metal.