Why do Jupiter’s moons have so much water by mass? Did all the bodies in the solar system start out with this much water and the planets closer to the Sun simply lost it to space?
tl;dr: They have more water because they captured it as ice, and it’s easier to hold onto ice than water vapor. Planets (and by extension, moons) beyond the frost line were formed with ice as a part of their cores, so they in a sense started off with more water than terrestrial bodies closer to the sun.
A surface level explanation boils down to one thing: the frost line.
There is a line (roughly twice the Sun-Mars distance at ~3 AU) beyond which water can exist as ice for an indefinite amount of time exposed to the Sun (that of course is not to say ice can’t exist inside this region, but rather that it needs accommodations like being obscured from the Sun for large chunks of time).
Because water can exist as a solid beyond this point, it can (mixed with rocks and metals) contribute to the formation of planetesimals which leads to planets, leading to much larger planets (gas giants).
Inside the line, water is vaporized and only kept by planets with masses large enough to hold onto it.
As you can see, by this reasoning gas giants (and by extension meteors, moons, dwarf planets etc) beyond the frost line are just naturally going to have more H2O because it’s a lot easier for a planet to hold onto ice than water vapor, seeing how the latter can escape if the Boltzmann distribution of its speeds has a big enough tail beyond the escape velocity of the body.
Once ice is captured, methods like geothermal heating can melt ice closer to the core of the body, leading to a situation like Europa where there is believed to be liquid water under its surface.
While I’ve probably glossed over a lot of important details, this is a (hopefully) digestible explanation.