How long does it take for chest and arm muscles to atrophy if you stop working out with weights?

Double the time. I agree with the original answer. The concern is not true atrophy but the loss of power and performance. The typical rule is it takes twice as long to get back to where you were as the duration of the absence. So if you missed 2 weeks, expect a 4 week interval of hard work to get back to where you were.
Mushy Muscles. True atrophy takes years of disuse to occur. What you may be referring to is actual power. Muscle power depends upon recruitment of fibers. Working out helps create new fibers and creates recruitment of more fibers for a particular action. When you cease these activities, certain fibers called fast and slow twitch operate differently and as a result power will diminish.