The amp meter is moving when you turn the headlights on because the headlights are using power (amps) and the guage is simply showing that usage. That in itself is not a problem.
If you lights are dim it is probably because either your switch or wire are too small to carry the required current (measured in amps) and therefore you have voltage drop which results in dim lights.
The purpose of a relay is to act as a remote switch. If the relay is big enough (capacity, not physical size) and your wire is also big enough the relay could solve your problem.
Are you headlights something other than stock? If so they may require more power than the stock switch and wiring will support.
What size wire are you using? What is the rating of the fuse you are using? What is the rating of the switch? And what is the rating of the relay?
