"They" are doing a theoretical analysis in financial economics. The analyst does a calculation to decide how much risk various investments have. The analyst also decides what weight each investment should have. The analyst does not think that all of these investments are equally important in the overall picture.
We say that the analyst "gives" each investment its own proper weight. We can also say the analyst "assigns" each investment its own weight, or "puts" a different weight on each investment.
If investment X has a risk value of 10 and investment Y has a risk value of 20, then their average is 15. However, if we give X a weight of 80% and give Y a weight of only 20%, then their weighted average is 12.
If "tax equity" investments are riskier than the rest of the portfolio and we quadruple their weight in some formula, then the whole portfolio will be riskier.