Risk budgeting/coefficients/covariance/variance

Struggling with risk budgeting/coefficients/covariance/variance.

Typically the question has been ‘what % of total risk is explained by a factor’ (example page 345 of Vol.3).I understand that once you have the variance of a factor you divide by the total variance to determine the amount of total variance it explains, but I am not understanding:

a) when I look at the answer it suggests that the coefficient is the ‘weight’ I am not understanding why?
b) I have seen a similar equation using assets and a portfolio is it conceptually the same only that you replace the assets with factors and plug those number into the equation instead?

Thanks