jnasr wrote:
So the formula for 1983 should return 0, 1984 should return 22.5%

How do you figure that!? I compute 19.3% approximately, namely:
(200*22.5% + 150*15%) / (200 + 150).

jnasr wrote originally:
A B C
1 Year Size Return
2 1983 100 20%
3 1983 75 10%
4 1984 200 22.5%
5 1984 150 15%
6 1985 300 10%

I would like to be able to create a formula that would allow me to
calculate the weighted average of each year's returns if the size is
greater than 100.

Does the following satisfy your needs. Starting in D2 (and copy down),
put:

=IF(A2=A1, "",
SUMPRODUCT(--(A2:$A$100=A2),--(B2:$B$100100),B2:$B$100,C2:$C$100) /
SUMPRODUCT(--(A2:$A$100=A2),--(B2:$B$100100),B2:$B$100)

This puts a number into the D cell that corresponds to the first row of
a year; e.g. D2, D4 and D6. It puts a blank into other D cells; e.g.
D3 and D5.

The first condition (A2:$A$100=A2) is true only for the first row of a
year. The second condition (B2:$B$100100) is the size constraint that
you specify. In the numerator, the product of the third and last
parameters computes the total number of returns (subject to the other
conditions). In the denominator, the last parameter computes the total
"size" values (subject to the other conditions).

This presumes that "size" is a quantity count, not a category (e.g.
size in millimeters).