Are is most certainly of North Germanic origin. It appears in Norwegian, Swedish, Danish and Icelandic but doesn't appear in either German or Dutch. Of course it's present in English. Interestingly, be is actually of North Germanic origin not West Germanic, but to make things even stranger to some is that the German equivalent which in German is
sein also appears in Norwegian and Danish. The question this raises is that given that all these languages descend from proto-Germanic, are there presence due to having been originally in the proto-language and lost only to be re-adopted by cross-fertilization or were they just retained by some of the descendant groups or were they adopted from another language group or autochthonous in nature. We know in the case of English it was the prior.
As for Frisian, I don't know, but one must take note of the fact that there definitely was a Norse influence in Frisia.
The question this raises is that given that all these languages descend from proto-Germanic, are there presence due to having been originally in the proto-language and lost only to be re-adopted by cross-fertilization or were they just retained by some of the descendant groups or were they adopted from another language group or autochthonous in nature. We know in the case of English it was the prior.How do we know this in the case of English? If I'm not mistaken, the only NG influence on English would have come from the Danish invasion in the late 1st millennium. But Anglo-Saxon had variations of are before that. I seem to recall the AS version of the Lord's Prayer opening as: "Faeder ure, thu the eart in heofonum..."
Interestingly, even though be didn't form the infinitive in German or Dutch, it still existed, as in "Ich bin, du bist". So that leads me to wonder if these forms existed in all the Germanic languages, but came and went at different times for reasons as yet unknown. If so, then cross-fertilization may not have been a factor.
Besides, it seems rather odd to me that something as basic as the verb "to be" would ever be incorporated from another language. Usually words that come from other languages aren't of the everyday variety, but are used to express some concept that doesn't exist or isn't fully developed in the original language. Why would a language all of the sudden start using another language's word for "are"?