upgrading to heavier wire will increase your light output on standard halogen systems. The manufacturers run the thinnest wire they can to save weight, cost, space, etc. Thinner wires have more voltage drop. Less voltage = less output from filment bulbs.
Ideally you would run a relay at the lamp housing. That way you can have they shortest possible run of thick wire and use thin wire to trigger the relay. http://www.sylvaniaautocatalog.com/s..._tech_info.htm
"In incandescent lamps, the filament resistance, temperature, current, watts, light output, and life are all greatly affected by the voltage. Empirical equations are available, relating those parameters to voltage over ranges of as much as 10% from nominal voltage. The designer may improve one parameter by changing the voltage, but in doing so shifts all the other parameters. For example, the life varies so that a small decrease in voltage will greatly extend the life; but the light output will simultaneously decrease as the fourth power of that voltage. The nomograph and curve diagrams below show the interrelationships of current, candlepower, and operating life to voltage."