Is it normal that a node in a weighted directed graph gets a higher measure of betwenness centrality when its edge weights are lower?

Question

I have a weighted directed graph and I use cytoscape.js library to measure betweenness centrality of the nodes. However, I noticed that the nodes that have lower edge weight actually tend to have higher betweenness centrality even if they are positioned the same way in the network as the other nodes with the higher edge weight.

Shouldn't it be the other way round?