For various reasons, cohort studies generally forgo probability sampling required to obtain population representative samples. However, such cohorts lack population representativeness, which invalidates estimates of population prevalences for novel health factors that are only available in cohorts. To improve external validity of estimates from cohorts, we propose a kernel weighting (KW) approach that uses survey data as a reference to create pseudoweights for cohorts. A jackknife variance is proposed for the KW estimates. In simulations, the KW method outperformed two existing propensity-score-based weighting methods in mean-squared error while maintaining confidence interval coverage. We applied all methods to estimating US population mortality and prevalences of various diseases from the non-representative US National Institutes of Health-American Association of Retired Persons cohort, using the sample from the US-representative National Health Interview Survey as the reference. Assuming that the survey estimates are correct, the KW approach yielded generally less biased estimates compared with the existing propensity-score-based weighting methods.