Are Water Spiders Web Weavers?

Yes, but not for the  same purpose.   Instead of
a web, they weave a retreat, a big silken bag
anchored to plants, underwater.
When it is finished,the spider comes up,
captures a bubble of air with the fur on it's
belly and take it down.  Once back at
the bag, it release the bubble under the bag.  
Eventually.the retreat will fill with air and serves as
both a home and a launch site.   The spider swims
very well so when prey (water insects) comes near,
it catches it, bites it and, then retreats back home
with it for a hearty meal.  Mating takes place inside
and, later, the home and launch site becomes a
nursery as well.