Is a Water Weird invisible while attacking in water or does the invisibility stop while in combat?
If the creature remains invisible, all attacks against it are at disadvantage and attacks the Water Weird makes have advantage, right?
The Water Weird's ability is as follows:
Invisible in Water. The water weird is invisible while fully immersed in water.
There are no clauses or conditions in there that would prevent this ability from working. Compare this to, for example, the Invisibility spell:
The spell ends for a target that attacks or casts a spell.
If the Water Weird's invisibility was meant to cease functioning on attacking, it would have to include a similar clause. The statement in the Water Weird's ability is absolute - if it's fully underwater, it's invisible.
As you say, this means that attack rolls against the Water Weird will have disadvantage, and its attack rolls will have advantage.
Note that for this ability to apply, the Water Weird has to be fully immersed, so if even a bit of it is poking up out of the water, its invisibility will not function.