What is the current best state of the art algorithm for graph embedding of directed weighted graphs for binary classification?
I'm no expert myself, but recently (i.e. this is true to 2019), I've heard (at a meetup from an expert) that Node2Vec is the SOTA. 

Here's a link to a post on Medium explaining it - basically, Node2Vec generates random walks on the graph (with hyper-parameters relating to walk length, etc), and embeds nodes in walks the same way that Word2Vec embeds words in a sentence.

Note that since random walks are generated on the graph, intuitively you don't have to use edge weights, and can use multiple edges.

P.S. There's an older (2014) algorithm for this, called "DeepWalk", which I don't know much about but is supposed to be similar, simpler, and not as performative. I'm just adding this in case you want to search the term.