What ever happened to the Dwarves after the Tird Age

[Legolas]

They evolved into Ewoks, didn't they?

Anyway, from part III of Appendix A:

Dís was the daughter of Thráin II. She is the only dwarf-woman named in these histories. It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people. They seldom walk abroad except at great need, They are in voice and appearance, and in garb if they must go on a journey, so like to the dwarf-men that the eyes and ears of other peoples cannot tell them apart. This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves 'grow out of stone'.
It is because of the fewness of women among them that the kind of the Dwarves increases slowly, and is in peril when they have no secure dwellings. For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.