Old English "to be" was wesan, from Proto-Indo-European *h₂wes- "to live, dwell" and the source of was and were. The ODEE says "The orig. meaning is 'dwell, remain', and the use of this base is therefore appropriate to the imper[fect] (OE. wes, pl. wesaþ) and the [past]." Other forms of "to be" come from *h₁es-, which I've already written about.
PIE *bʰeuH- "to be, exist, grow" is the source of another Old English verb, bēon "to be", and which survives in be, been and being. *bʰeuH- is also the source of the Latin stem fu-, used in some conjugations of esse "to be", including the future participle futūrus - the source of future. In Greek, *bʰeuH- became φύω "to bring forth, make grow", and physics.
The origin of are is uncertain; the ODEE says "of unkn. origin", and the AHD says it's from *h₁er- "to move, set in motion". Old English had eart in the second person singular present indicative, and earon, earun, earan and aron as plural forms; it seems likely that these are from *h₁er- and are the source of are.
Romance languages developed another verb for "to be" from Latin stāre "to stand" (from *steh₂- "to stand"). So Italian and Spanish have 2 verbs each: stare and estar (from Latin stāre), and essere and ser (from Latin esse from *h₁es-). In French it seems that the two verbs were conflated into one: étais is from stāre and est, sont, serai are from esse.