Let g = (V, E, ${mu}$) be a weighted directed tree, where V is a vertex set, E is an edge set, and ${mu}$ is ${sigma}$-finite measure on V. The tree g induces a composition operator C on the Hilbert space $l^2$(V). Hand-type directed trees are defined and characterized the weak hyponormalities of such C in this note. Also some additional related properties are discussed. In addition, some examples related to directed hand-type trees are provided to separate classes of weak-hyponormal operators.