In the Neveu-Schwarz sector, the worldsheet fermions can be expanded as

$$ \psi^I(\tau,\sigma) \sim \sum\limits_{r\in Z+1/2}b_r^Ie^{-ir(\tau-\sigma)} $$

and the total mass squared operator can then be written as

$$ M^2 = \frac{1}{\alpha'}\left( \frac{1}{2} \sum\limits_{p\neq 0} \alpha_{-p}^I\alpha_p^I + \frac{1}{2}\sum\limits_{r\in Z+1/2} r \, b_{-r}^I b_r^I \right) $$

The first sum gives the contribution of the bosons, the second one the contributions of the fermions.

Why are the summands in in the fermionic part multiplied by $r$, how does this factor come in mathematically? Does this have something to do with the Pauli exclusion principle?

The same thing issue appears with the fermionic part mass operator in the Ramond sector, where I dont understand it either ...