How to judge time between cracks when roasting I just roasted beans at home for the first time and have a question about the expected timing between cracks.  I roasted 1 cup of beans in a Crate and Barrel stovetop popcorn popper on the side burner of my outdoor grill with the heat on high.

From what I had researched ahead of time, I was expecting to hear the series of first cracks, then pause of a couple of minutes, then faint cracks.  Instead though, the first cracks started around the three minute mark and continued for the next four minutes.  I can't tell if the second cracks ever started, since the sound never stopped from the first round.

The color and texture of the roasted beans is close to other store-bought beans, but they smell burnt.  I kept thinking I should take them off the heat but thought it might be too early and I hate weak coffee.

Should there be a space of time in between cracks?  Does this sound like I had the heat up too high?  I was stirring constantly, about one turn every 2-3 seconds.
Distinguishing between end of first crack and the start of second crack can be very tricky. A lot has to do with the variety of beans being roasted and your heat application.

What I think happened to you was that you lost control of your heat. At first crack your beans become exothermic (give off heat) and you didn't reduce your heat. What happened then is that you had too much heat at raced through the "development" time in your roast profile. 
To correct this you should reduce your heat at the start of first crack and develop the flavor by how much/long  you let the beans go for before taking them off the heat.
This is a critical time for your roast because your are developing the flavor in your roast by time and roast level. How you apply heat changes from variety to variety and darkness. 
Take the time to read up on roasting theory.

Here is a good basic guide: A basic roast profile guide for home coffee roasters.

Good luck