I'd say you are asking two different questions.  Let me restate them for you:

1) How do weed seeds know when it is time to germinate?

2) Why do domesticated seeds germinate uniformly, while seeds of weeds germinate over a longer period of time

Is that fair? separately them out as two different questions?

In response to #2, I would say the reason crop seeds germinate over a shorter period of time is due to genetic selection - man involved in the selection of seeds that germinate uniformly.  I'd venture to guess that if you did a DNA analysis of, say, 100 grain crop seeds/plants... you would have very little diversity in the genetic makeup.  Whereas, if you did a DNA analysis on 100 plants of a weed species, you would see a lot more genetic diversity.  I would think this would have an impact on how & when these seeds germinate.

In response to #1, weed seeds germinate in response to temperature, light (or lack thereof), soil moisture, season...... a multitude of factors..... and how that weed seed responds to the environment around it is coded into its DNA.

That's my answer to your question.