How to test dependent means with unequal sample size? Weighted Paired T-test?

Does a Weighted Paired T-test exist?

I am comparing the percent of a population that are juvenile between 'Autumn' and 'Spring' at many sites. The Sample size (n) is variable among the sites and between the seasons. Sample data:

Site___Fall %__n_____Spring %__n

If samples were equal I would use a paired T-test but since they are not, I would prefer to use weighted means. Sample size would be used as weight because I have greater confidence in them. I need to test non-independent weighted means but I am not aware of a 'Weighted Paired T-test.' What statistical test do you recommend?

Thank you

p.s. people have suggested using linear regression for this, but I don't know how or if it's even right.
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