  In this article, we introduce a category of weak Lie 3-algebras with suitable
weak morphisms. The definition is based on the construction of a partial
resolution over $\mathbb{Z}$ of the Koszul dual cooperad of the $\textrm{Lie}$
operad, with free symmetric group action. Weak Lie 3-algebras and their
morphisms are then defined via the usual operadic approach---as solutions to
Maurer--Cartan equations. As 2-term truncations we recover Roytenberg's
category of weak Lie 2-algebras. We prove a version of the homotopy transfer
theorem for weak Lie 3-algebras. A right homotopy inverse to the resolution is
constructed and leads to a skew-symmetrization construction from weak Lie
3-algebras to 3-term $\textrm{L}_\infty$-algebras. Finally, we give two
applications: the first is an extension of a result of Rogers comparing
algebraic structures related to $n$-plectic manifolds; the second is the
construction of a weak Lie 3-algebra associated to an CLWX 2-algebroid leading
to a new proof of a result of Liu--Sheng.
