Remarks on the plus-minus weighted Davenport constant

For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted ${\mathsf{D}}_{\pm }(G)$, is the smallest $\mathrm{\ell }$ such that each sequence $g_1\mathrm{.}\mathrm{.}\mathrm{.}{g}_{\mathrm{\ell }}$ over $G$ has a weighted zero-subsum with weights +1 and -1, i.e., there is a non-empty subset $I\subset \{1,\mathrm{.}\mathrm{.}\mathrm{.},\mathrm{\ell }\}$ such that ${\sum }_{i\in I}{a}_i{g}_i=0$ for $a_i\in \{+1,-1\}$. We present new bounds for this constant, mainly lower bounds, and also obtain the exact value of this constant for various additional types of groups.