watch someone's smoke

watch (one's) smoke

To observe the successful results of accomplishments of one's endeavors or activities. He told us to watch his smoke when he left to set up his own company. Everyone is watching their smoke to see how they do in the competition.
See also: smoke, watch

watch someone's smoke

observe another person's activity.
The implication of this phrase is that the activity in question will be so fast and furious that smoke will be generated.
1947 P. G. Wodehouse Full Moon Look at Henry the Eighth…And Solomon. Once they started marrying, there was no holding them—you just sat back and watched their smoke.
See also: smoke, watch