Do the words 'tied' and 'tight' have a common origin?

Per the Oxford English Dictionary, the Concise Oxford Dictionary of English Etymology, and the Old English Translator, tie comes to us from the Old English tigan, related to the Old Norse taug (rope) and *tegja (to draw, as in drag). Tight comes to us from the Old English þíht, related to the Old Norse þehtr, tightly woven. So the two words descend to us from different Old English parents.

But the OED advises us to consider the obsolete word tee, meaning draw or drag, which comes to us from the Old English teon (past participle togen, related to the Old Norse toginn). The parent of this word is a "primitive Aryan [i.e., Indo-European] word", which gave rise to the Latin ducere (to lead or draw) and to words of similar meaning in the family of Germanic languages. Says the OED

Derivatives of the same root survive in taut, team, tie, tight, tough, tow, tug.

So the two are related if you go back far enough.

As an Addendum to deadrat's answer:

According to The Families of Words by Mario Pei (Harper Brothers, 1962), tie and tight both come from the PIE root *deuk, "to draw, pull". The root on the Germanic side also gives us tow, tug, taut, team, tether, among many other words, including wanton and Herzog. On the Latin side, we get duke, educate, and conduit, among many other words and some common suffixes (e.g., -ducive and -ductor).

So far, agreement. But then Etymoline (which I had to check, darn it!) differs in the PIE roots of tie and tight.

Tie, From Etymoline

Old English teag, "cord, band, thong, fetter," literally "that with which anything is tied," from Proto-Germanic *taugo (cognates: Old Norse taug "tie," tygill "string"), from PIE *deuk- "to pull, to lead" (cognates: Old English teon "to draw, pull, drag;" see duke (n.)).

Tight from Etyomoline

c. 1400, tyght "dense, close, compact," from Middle English thight, from Old Norse þettr "watertight, close in texture, solid," and also from Old English -þiht ....., both from Proto-Germanic *thinhta- (cognates: Middle High German dihte "dense, thick," German dicht "dense, tight," Old High German gidigan, German gediegen "genuine, solid, worthy"), from PIE root *tenk "to become firm, curdle, thicken"

Etymoline agrees that taut, tow and tug come from the same PIE root as tie *deuk

It would be nice to have better than two out of three votes for the common PIE root of tie and tight.