In this work, we study the character amenability of weighted convolution algebras $ell^{1} (S,omega)$, where $ S $ is a semigroup of classes of inverse semigroups with a uniformly locally finite idempotent set, inverse semigroups with a finite number of idempotents, Clifford semigroups and Rees matrix semigroups. We show that for inverse semigroup with a finite number of idempotents and any weight $ omega $, $ell^{1} (S,omega)$ is character amenable if each maximal semigroup of $ S $ is amenable. Then for a commutative semigroup $ S $ and $ omega(x)geq 1$, for all $ xin S $. Moreover, we show that character amenability of $ell^{1} (S,omega)$ implies that $ S $ is a Clifford semigroup. Finally, we investigate the character amenability of the weighted convolution algebra $ ell^{1} (S,omega)$, and its second dual for a Rees matrix semigroup.