  For $(G,+)$ a finite abelian group the plus-minus weighted Davenport
constant, denoted $\mathsf{D}_{\pm}(G)$, is the smallest $\ell$ such that each
sequence $g_1 ... g_{\ell}$ over $G$ has a weighted zero-subsum with weights +1
and -1, i.e., there is a non-empty subset $I \subset \{1,..., \ell\}$ 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.
