I will be using the spelling "khvedodah" (Avest. khvaetvadatha) in correspondence with how modern Persian is normally transcribed (the "kh"/"x" is roughly the same sound as in "Khomeini" or "Khorasan" or the ch in "Loch"). I should note before I begin that the word does occur in some very old Avestan material (Yasna 12.9) but in context it reads like a later insertion.

A bit on its background and origins:

The first recorded explicitly close-kin marriage (which I will define as including (half-)sibling/sibling, parent/child, uncle/niece, aunt/nephew, and cousin/cousing) in Persian history is that of Cambyses, son of Cyrus the Great. According to Herodotus, he fell in love with and married his sister Atossa, Curiously, Herodotus notes that this was not in line with Persian custom - specifically, he says that the learned men of Cambyses' court had found no law explicitly permitting it - but the same learned men had concluded that on the other hand, the Persian Great King could do whatever he wanted, and so Cambyses proceeded. There are other recorded marriages between people of the same clan as far back as the Avesta (King Vishtaspa), but that doesn't necessarily mean close-kin marriagae.

There is some difficulty associated with the first Achaemenid Great Kings in that we can't be certain they were Zoroastrian, or even Persian (Atossa is the only Iranian - specifically it is Avestan - name given before Darius. Whereas Cyrus, Cambyses, et cetera are probably Elamite names), and therefore I won't dwell too much on Cambyses, but merely conclude that we in either case cannot trust that Herodotus was doing anything but projecting his own biases.

The other interesting ancient mention comes from Xanthos of Lydia, one of Herodotus' contemporaries quoted in a later work (sorry, I forget, let me know if you want me to look up who quoted him) as saying that the Magians (a tribe of the Medes) were known for cohabiting with their mothers, daughters, and sisters. Which, unfortunately, is also very little to go on.

It is once we get to the Parthian period that we get certain attestation of sibling marriages from Parthian king lists, from Arsaces I and onward, as well as in lists of marriages among their vassals and neighbours (such as Armenia, which might have practiced some form of Zoroastrianism at this time). We also find it recorded in Christian tirades against the Sasanian kings as example of their sinfulness (while, amusingly, the Sasanians held these marriages up as expressions of their piety!).

However, the Parsi communities who settled in Gujarat found that the Hindus disapproved even of cousin marriages, and this is a recurring matter in Pahlavi (Middle Persian) literature of this age. There is to my knowledge only a single record of a brother-sister marriage in the post-Sasanian literature (specifically in the Rivayat of Adurfarnbag-i Farrokhzadan). Gujarat came under Muslim rule in the early 14th century, and according to contemporary texts this made khvedodah easier, but at this point it was apparently restricted to first-cousin marriages. According to administrative records, which exist only from the 18th century on, this was the most preferred form of union.

I don't know off-hand if it has persisted in recent decades; it should be noted that there has been a lot of change and tension within Parsi communities over their strict rules of inter-community marriage for women, so I wouldn't take it for granted. I'm afraid I can't help you more with what is said about it within Parsi communities today; I could ask the Parsis I know, but that would be entirely anecdotal.

I hope that answered your question - Khvaetvadatha can be any form of close-kin marriage up to first cousins, and which form has been preferred has varied historically. Let me know if you want more precise citations of Pahlavi texts and I can dig them out.

I mainly relied on Boyce's Zoroastrians: Their Religious Beliefs and Practices which summarizes Zoroastrianism from its inception to the present day, as well as cross-checking with source material. The Encyclopedia Iranica is useful if you want to read more: www.iranicaonline.com