We purchased a Harbor Breeze fan with light fixture, but did not see that the wattage output was only going to be 40 watts. We need more lighting in our room. We have tried bigger watt bulbs but the fixture starts to blink and then goes dim(back to the 40 watt output). How can we change that?

Change the fixture to something that is listed to handle a higher wattage lamp.

Fixtures, sockets, assemblies, are tested by UL as the manufaturer lists them, if your is only 40 watts, then that is all the fixture can handle safely.

Or use a compact fluorescent lamp that will give the light output you need, these draw much less wattage as the comparable incandescent lamp.