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Let $R$ be a commutative Noetherian ring, $\fa$ be an ideal of $R$ and $M$ bean $R$-module. The main purpose of this paper is to answer the Hartshorn'squestions in the class of weakly Laskerian modules. It is shown that if $s\geq1$ is a positive integer such that $\Ext^j_R(R/\fa, M)$ is weakly Laskerian forall $j\leq s$ and the $R$-module $H^i_\fa(M)$ is $FD_{\leq 1}$ for all $i < s$,then the $R$-module $H^i_\fa(M)$ is $\fa$-weakly cofinite for all $i <s$. Inaddition, we show that the category of all $\fa$-weakly cofinite $FD_{\leq 1}$$R$-modules is an Abelian subcategory of the category of all $R$-modules. Also,we prove that if $\Ext^i_R(R/\fa,M)$ is weakly Laskerian for all $i\leq \dimM$, then the $R$-module $\Ext^i_R(N,M)$ is weakly Laskerian for all $i\geq 0$and for any finitely generated $R$-module $N$ with $\Supp_R(N) \subseteq V(\fa)$ and $\dim N \leq 1$.

Hartshorne's questions and weakly cofiniteness