There is some indirect evidence that weightlifting improves productivity, assuming that cognition is an important determinate of productivity.
For example, a recent meta-study, Lifting cognition: a meta-analysis of effects of resistance exercise on cognition by Jon-Frederick Landrigan, Tyler Bell, Michael Crowe, Olivio J. Clay, Daniel Mirman, reports that:
Results revealed positive effects of resistance training on composite cognitive scores (SMD 0.71, 95% CI 0.30-1.12), screening measures of cognitive impairment (SMD 1.28, 95% CI 0.39-2.18), and executive functions (SMD 0.39, 95% CI 0.04-0.74), but no effect on measures of working memory (SMD 0.151, 95% CI - 0.21 to 0.51).
That much closer to what I was hoping to find than I found initially, and I’d say it passes the initial bar. A few knocks against it are the focus on the elderly (the mediate age was 70) and the high variability in the outcomes. I’m not familiar enough to know what to expect, but those plots look all over the place to me.