weave has lots of very happy users who find that weave is plenty fast enough for their purposes, see eg http://blog.weave.works/2015/02/24/get-your-kicks-on-cloud66...
the strong points of weave network, as it is right now, are ease of use (not to be sniffed at), and enormous flexibility. it is really quite easy to create an application involving containers, that runs anywhere and does not commit you to specific architectural choices...
typically though, one weave network might be used by one app, or just a few. but you might run a lot of weave networks
weave works very nicely with kubernetes - later I shall dig out a few links for this
in our own tests, throughput varies by payload size; we tend to think of weave-as-is is best compared with using, for example, amazon cloud networking directly
for users with higher perf needs, we have a fast data path in the works, that uses the same data path that ovs implementations use... the hard problem to solve here is making that stuff incredibly easy and robust w.r.t deployment choices -- see above :-)