From an unattested English dialectal word *weak (“moist; moisture”) + -y. Compare voky, woky.
*Weak is from Middle English *weke, *wak, *wok, from Old Norse vǫkr (“moist; damp; wet”) and Old Norse vǫkvi, vǫkva (“moisture; juice”), from Proto-Germanic *wakwaz (“moist”) and *wakwô, *wakwijô (“moisture; wetness; open water; icehole”), from Proto-Indo-European *wegʷ- (“wet”).
Germanic cognates include Scots wak, wakke, waik (“moist; damp; wet", also "moisture; wetness”); Dutch wak (“icehole; blowhole”) and its earlier form, Middle Dutch wac (“flexible; liquid; moist; soft”); Middle Low German wake (“hole in the ice; open water in the ice”); Swedish vak (“hole in the ice”); Icelandic vökur (“moist”) and vökvi, vökva (“fluid”).
Indo-European cognates include Latin ūmeō (“to be wet, moist or damp”), whence English humid, humidity, and humidify; Ancient Greek ὑγρός (hugrós, “wet; moist; fluid”, adjective), whence English hygro-; Sanskrit उक्षति (ukṣáti, “to wet; moisten; sprinkle”).
weaky (comparative weakier, superlative weakiest) (UK dialectal, Northern England, Scotland)