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1670s, probably from Spanish or Portuguese alcatraz "pelican" (16c.), perhaps derived from Arabic al-ghattas "sea eagle" [Barnhart]; or from Portuguese alcatruz "the bucket of a water wheel" [OED], from Arabic al-qadus "machine for drawing water, jar" (from Greek kados "jar"), in reference to the pelican's pouch (cf. Arabic saqqa "pelican," literally "water carrier"). Either way, the spelling was influenced by Latin albus "white." The name was extended, through some mistake, by English sailors to a larger sea-bird (order Tubinares).
Albatrosses were considered good luck by sailors; figurative sense of "burden" (1936) is from Coleridge's "Rime of the Ancient Mariner" (1798) about the bad luck of a sailor who shoots an albatross and then is forced to wear its corpse as an indication that he, not the whole ship, offended against the bird. The prison-island of Alcatraz in San Francisco Bay is named for pelicans that roosted there.