Other than the light/dark change that occurs with day and night, one small link they would have to space is that comets/meteors would still come in on occasion. The second thing that could give them a lot to ponder is the effect of distance from the center of their planet on gravity and atmospheric thickness.
Well below cloud level it is easy to notice that the density of the air on earth varies a lot; a one mile change in elevation is noticeable in its effect on your stamina just walking around. Additionally, they might have mountains/balloons that get them far enough from the center of their planet to measure gravitational differences from the surface. These two facts could suggest a 'nothingness' beyond the clouds. In contrast, the occasional appearance of meteors/comets as well as the existence of sunlight would show that there had to be a fair amount of stuff beyond the clouds.
You might be able to roughly work out the distance to the sun by solving a system of equations related to light/heat output of a body of a given size at a fixed distance, the gravitational impact of the interaction of their planet and the sun at a fixed distance. If they can see a faint outline of the sun, this would further constrain where it could be. 921
Once they realize how big the sun is, then you can learn that comets/meteors are either orbiting the sun or flying in from some more distant part of the nothingness. Even if the latter is true, some should wind up orbiting instead of hitting the planet; this might let them imagine other planets in the solar system. You can see the effects of planets in each other's orbits, and I can imagine that a sufficiently detailed and really long term study of the tides of their own planet might produce data showing the impact of nearby planets on their moon, assuming they have one.
All this study of things orbiting would probably draw some interest into the question of whether or not something was orbiting them. They might reasonably come to look at tides as a potential source of information about celestial bodies orbiting their planet.
As others have mentioned, the possibilities grow substantially once you can study light outside the visible range.
People have mentioned "awe" and "wonder" as possible reactions to discovering the universe. I'd like to suggest that terror is at least as likely. The sudden realization that the universe is unimaginably vast would probably create a lot of concern about who and what else is out there. 99