Talk to your neighbors about the lawn. IMO, worrying about weeds is a waste of time. If it's green, it's good. When we moved into our house, the sprinkler system was set to way too frequently. You're better off watering longer less frequently. That encourages deeper roots, which can withstand no water better. If you always just sprinkle the surface, you'll have shallow roots on your grass which will die quickly.

A lot of it, though, it dependent on your soil and climate.

I would never put down herbicide. You don't want a lawn that takes constant applications of chemicals. It's bad for the environment, the water, and you.

To measure how much water your grass is getting, get a rain gauge (they're pretty cheap) and measure .

I concur with Sigrid. Burmuda is tough and can make it on far less water than most people use on it. As Sigrid points out much depends on combination of conditions so for that reason I suggest experimenting. Pick a zone to use less or more water then observe results. As for weeds,the local tv people once interviewed an old gent that garden club awarded lawn of the month following almost 90 days ban on watering. When asked what kind of grass he had, Dallis Grass he answered. The stuff stays green but must be mowed daily to clip seedhead off.