It has been known for some time that there are physiological changes associated with spaceflight- bone and muscle mass decrease, and the distribution of fluids in the body changes as well, all in response to the decrease in gravity. This is why astronauts ride exercise bikes when they are in space.
Perhaps the most accessible (and trustworthy) resources I have been able to find about the effects of low gravity on the molecular behavior of cells is from the NASA Twins Study, where one twin of an identical twin pair was sent into space for one year, while his brother remained on Earth. Before and after the year in space, the brothers were sampled and tested in all kinds of ways and interesting changes in gene expression and metabolism were found. For example, many genes changed expression levels in the brother who went to space, but they quickly returned to baseline after return to earth. However, a small number of genes remain at changed levels of expression, suggesting that long-term exposure to low gravity does change patterns of gene expression. It is important to note that these changes are not at the genome level; rather, they are attributed to changes in epigenetic regulation of the genome. You can see a summary of these results here.
My knowledge of evolutionary biology is too thin to comment fully on the part of your question that asks about unused genetic information from earlier stages of evolution, but I would expect that if gene expression and cell behavior changes in low gravity, that several generations of humans living entirely in zero or reduced gravity would be trending toward genetic difference from Earth-bound humans. You wouldn't necessarily see changes in an individual, but over time they could accumulate and cause different regions of the genome to be expressed in ways that humans on Earth do not experience.