  We study the intersection theory on the moduli spaces of maps of $n$-pointed
curves $f:(C,s_1,... s_n)\to V$ which are stable with respect to a weight data
$(a_1,..., a_n)$, $0\le a_i\le 1$. After describing the structure of these
moduli spaces, we prove a formula describing the way each descendant changes
under a wall crossing. As a corollary, we compute the weighted descendants in
terms of the usual ones, i.e. for the weight data $(1,...,1)$, and vice versa.
