"Favored" vs. "favorited"
Solution 1:
You should use the verb favourite and not favour. Favour means show an approval or preference for, while favourite means record to enable quick access. It is true that you favourite a video on a website if you like it, but the sense you want to convey here is not that you like the video but that you mark the video in some way. Of course, the past tense of favourite is favourited.
Solution 2:
As Jasper Loy pointed out in the other answer, favorite/favourite has entered into the vocabulary as a verb in British English and even been recognized by the OOD, but I thought I'd provide the American perspective:
Favorite is traditionally a noun or adjective. Although its use as a verb would certainly be understood, its use seems to be limited to certain websites (e.g. Twitter) and it would sound "wrong" to some ears. It does not appear in either M-W or dictionary.com at present.
Additionally, this NGram shows that while "favorite" may be a legitimate verb in some circles, its past tense has not found its way into the corpus.
American usage tends to prefer alternative constructions when it comes to UI design, such as "bookmark", "star" or the wordier "Add to Favorites".