You subtract the week's rain from the week's needed watering, unless it was a ludicrously tiny amount.

If
you are getting several times the needed water as rainfall, wait until a
moisture meter tells you the soil is drying out before your start
watering again.
And look at the grass, feel the soil ... does it look healthy? Is the soil damp an inch or two under the surface?

Here's my take on watering which accounts for all variables : rain, soil type, shade/sun, grass type etc.

http://lawniac.com/lawn-watering

Th easiest way to tell if your lawn need more water than the rain is supplying is to walk on it........if the blades bend over but don't spring back up right away, then it needs water.

Joe - I live in the same area as you and we aren't remotely near needing to water the lawns with all this rain. To answer your question, if it rains more than the recommended "deep and infrequent" then there's nothing you can do. If mother nature wants to try and sprout all your weed seeds with a lot of rain, all you can do is make sure you have thick, healthy grass and mow high.

jc411 brought up an interesting point I hadn't considered about a year ago. He asked why it seems that grass responds better to rainwater than to water from the tap. The discussion lead to the idea that rainwater is saturated with nitrogen from the atmosphere, so it is like getting a little jolt of foliar nitrogen application with each rain.

That's an interesting idea, I was thinking rainwater is much more acidic than groundwater, plus free of additives...I never considered atmospheric nitrogen

I'd heard it's partly because it's pH neutral, and has no chlorine, or flouride, etc. Or, ozone. Whatever the reasons, it's amazing how much better plants respond to it than city water.

Rain water is not pH neutral, it is slightly acidic due to the CO2 absorbed from the atmosphere.