If the Sun heated our atmosphere and the molecules began spreading apart and rising but our planet's gravity was too
weak to keep them down, what would happen?

the atmospere would drift off into space

none needed

then the molecules would be lost in space

Explanation:

Because if the molecule is spreading and rising and earth's gravity could not hold them down then the molecules would just slip away

and after water is usually warmed by the sun the water temperature raises and then evaporates .