In the past, slavery was a common practise, as was holding women and homosexuals in a lower moral standing. Violence was seen as honorable, and war and torture were more common. Values tended to be more communitarian/collectivist, and tradition was something that was highly respected.
Also, during the Industrial Revolution, (some) people in Europe went through a change in values (‘burgeois virtues’) that is known be a key to explain why it happened first in Europe, but not in China.
Here I present some theories that try to explain the nature of value change.
It is important to note that these theories do not address why morality is out there in the first place. That’s not their point. There are other theories that try to explain morality, or find its structure (In moral psychology there’s at least Haidt’s Social Intuitionist Theory, Greene’s Dual Process Theory, Kohlberg’s Moral Development Theory, and Mikhail’s Universal Moral Grammar).
These theories don’t try to explain why values change, they try to explain why they are how they are right now. The theories I gather below focus on why that change happens.
The Imposition theory ()
Societies with fitter values could conquer societies with unfitter ones, and impose their own. In the end, values that promoted societal capacity for domination (including intra-societal cooperation) would predominate.
Another channel would be that elites who hold power use it to influence societal values as to promote those values that benefit the elites.
Yet another one would be that succesful cultures spread their values via their cultural production (History books, movies, music, or even memes). This shapes values in other cultures.
The Cultural evolution theory (Hayek)
Values can change faster than genetic evolution would allow. While there is a core of moral values that evolved for a tribal setting, tribes that come to hold values that promote economic growth (respect for property rights, contracts, markets) will thrive and displace other societies. Succesful societies will end up being imitated by less succesful ones seeking to improve their conditions.
The Sentimentalist theory (Smith)
Human being have an innate desire for “mutual sympathy of sentiments”, and in general, a moral sense: it pleases us to see in others the same sentiments we have. This acts as a centripetal force that drives people towards rules that ensure that they ‘fit in’ with others’ values.
Increased cognitive abilities (through the Flynn effect) lead to a change in values. Either because those values simply come to be seen as true (Huemer), or because intelligence leads one to seek novel values from an evolutionary point of view (Kanazawa).
The Pathogen load theory (Thornhill)
Pathogens trigger a response in the form of different values (conservative ones, in general) that are useful to reduce infection and spread of disease.
Industrialization, economic development, and other changes in the economic structure of society lead to changes in societal values.
The Technological theory (, maybe same as Modernization)
Technology changes values through changing the cost/benefit structure of the different options available to an individual. Women may be regarded as lower status when there is no access to contraception or abortion, but when those are available, they come to be regarded as moral equals and granted rights accordingly.
EDIT: Perhaps this counts as evidence
You will have noticed what is problematic about all these theories taken together: That technological advancement, wealth, intelligence, low pathogenic load, and relatively liberal values have non-negligible correlations. So you would need to find a test that allows you to discriminate among then, though it is highly plausible that all of these theories have some influence in the resulting value change.