Unbalanced Sample Sizes

#1
Given two variables: one is a single estimate measured on one individual, the other is comprised of multiple samples taken from the same individuals (one-to-many dataset).

If the sample size varies by individual...

Is it reasonable to test for correlation by averaging for the second variable for each individual and accounting for the variation in sample size by specifying sample sizes as weights in a regression?

I realize that the most popular method for dealing with repeated measures of individuals is mixed effect modeling but for now my question is whether the above scenario is appropriate/plausible/reasonable.

thanks much.