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The weight of the water compresses a balloon on earth.
In space, since everything is falling together, the balloon wouldn't compress, it would expand because the atmosphere and water isn't compressing it. The surface tension of the water would allow it to envelop the balloon, so long as there is enough water to allow it to do so, otherwise it would want to gather into a spheroid because there aren't enough large surface defects on a balloon to "hold" the water. If the surface of the balloon was covered in sand glued to it, just enough water would film across the surface of the balloon.
Water gathering on a rough surface means you could drown in space if you had a drinking tube leak into your helmet and you couldn't drink the water fast enough to breathe.
This assumes you have relatively normal air temperature and pressure.
Things change quite a bit if you interpret space to mean "open vacuum of space"
Then you have to decide if you mean orbit exposed to solar radiation, or interstellar exposed to galactic radiation. Or just in null gravity with null radiation.
This question can have a lot of answers depending on context.
if you're not at relatively normal temperature and pressure, then you won't have liquid water anyway. and i don't think the kid was asking about water vapor or one of the various forms of ice.
He wants an explanation for his kid, no need to get into the weeds.
Depends on if the kid meant "in space" or "on something like the space station".
Kids being kids, he probably literally meant space, not realizing the implications of water (possibly) becoming gaseous from lack of pressure (I assume?).
For that age, it would be a good learning experience to explain in a spaceship vs in space - just not the triple point of water, or the different ices, etc.
Not realizing the implications, he probably meant "in zero gravity".