"There are proponents for using the moon for solar power. This may be a dumb question, but why would a solar power station on the moon that would beam (supposedly) harmless microwave energy to the earth be more cost effective than an earth-based solar power station?

It wouldn't be more cost efficent.

"Are the energy levels that diminished by the atmosphere that the expense of putting it on the moon is cheaper than building massive solar power collectors in say the Mojave Desert?"

I don't know the exact amount but I believe the atmosphere blocks about 1% of the usable solar energy- or some fairly insignificant number.

"Are weather conditions a factor? The moon has "weather" too."

Clouds can block a significant amount of solar energy, but generally people assume they block more than what is actually blocked- it's around 10%- of course, it varies depending on how thick the clouds are. The biggest factor of course is the nightime part of each day- I imagine it *might* be possible that solar panels could put closer to the arctic circle (thereby having more sunlight during the summertime when electrical energy demands peak) which could be more cost effective than solar panel somewhere in the southern state.
Of course weather on the Moon is mostly about the degradation of the solar panel by radiation and micro-metorites. On earth you also have weather potentially physically affecting the panels, such as tornados, lightening, hail, floods, etc.

As I have said before, power from space is not a near term solution for Earth's energy needs, rather it's a solution decades out rather than years out. A market for energy in space MUST be first established. It's crazy to want to provide electrical power from Space to Earth when you consider the low cost of energy available on the earth surface, in comparison to the present high cost of energy available in Space. On Earth you are looking at energy costs of around 10 cents per kw/hr, in space you are looking at energy costs of around 10,000 cents kw/hr.
Bringing the cost of electrical energy in Space down to around 1000 cent per kw/hr, would be fairly easy- if some governmental attention was directed towards doing this. Being able to buy large quantities of electrical power anywhere in the Earth/moon region at say 1000 cent per kw/hr would have a significant affect on any activity in this region. Getting the price down to 100 cents per kw/hr would be at least close to bringing about a "tipping point", in which in a relatively short period of time prices could be lower to be competive in Earth surface markets.
Water in Space is the KEY which opens this door. Water needs electrical power to convert into Rocket fuel. LH & LOX is a fairly portable and storable source of usable energy- not just for rockets. But what is needed in space is large quantities of rocket fuel which is significantly cheaper than the current price.