These measures are in general designed for unweighted graphs, and extending them to weighted graphs already is non-trivial. Extending them to signed weighted graph is even more difficult.
For instance, closeness and betweenness are both based on distances and shortest paths. In a (positively) weighted graph, the weight of a path already has several natural extensions: one may take the maximal weight of an edge in the path (think of weights as capacities), or the product of edge weight (think of weights as probabilities), their sum (think of weights as traversal costs), or others. If the weights may be negative, then such extensions become much more tricky. For instance, what may a path composed of positive and negative edges mean?
Still, if your think of degrees, and define the weighted degree as the sum of absolute values of edge weights, then a high weighted degree indicates that the vertex is highly (positively or negatively) correlated to others. However, it will make no distinction between a vertex highly correlated to a few others, and a vertex poorly correlated to many others.
In conclusion, I think there is no simple and general answer to your question. More information is needed on what you are modelling, what you want to capture with centralities. The best option may be to design a centrality measure tailored for your specific context and objective.
