Summary: We study two stacker crane cover problems and their variants. Given a mixed graph \(G=(V,E,A)\) with vertex set \(V\), edge set \(E\) and arc set \(A\), each edge or arc is associated with a nonnegative weight. The min-max stacker crane cover problem (SCCP) aims to find at most \(k\) closed walks covering all the arcs in \(A\) such that the maximum weight of the closed walks is minimum. The minimum stacker crane cover problem (MSCCP) is to cover all the arcs in \(A\) by a minimum number of closed walks of weight at most \(\lambda\). The min-max stacker crane walk cover problem (SCWCP)/minimum stacker crane walk cover problem (MSCWCP) is a variant of the SCCP/MSCCP with closed walks replaced by (open) walks. For the SCCP with weakly symmetric arc weights, i.e. for every arc there exists a parallel edge of no greater weight, we obtain a \(\frac{33}{5}\)-approximation algorithm. This improves on the previous \(\frac{37}{5}\)-approximation algorithm for a restricted case of the SCCP with weakly symmetric arc weights. If the arc weights are weakly symmetric, we devise the first constant-factor approximation algorithms for the SCWCP, the MSCCP and the MSCWCP with ratios 5, 5 and \(\frac{7}{2}\), respectively. Finally, we first propose a 4-approximation algorithm for the (general) MSCWCP.