Not to be pedantic, but I think 'laying' has a different etymology, namely this one (quote from the OED):
'lay, v.1 General sense: To cause to lie.
[OE. lęcgan = OFris. ledsa, lega, leia, OS. leggian (Du. leggen), OHG. lecken, legen (MHG., mod.G. legen), ON. legja (Sw. lägga, Da. lægge), Goth. (= OTeut.) lagjan, f. lag- ablaut-variant of OTeut. leg-: see lie v.'
OE = Old English, OFris.= Old Frisian etc.
'lay, v.1 General sense: To cause to lie.
[OE. lęcgan = OFris. ledsa, lega, leia, OS. leggian (Du. leggen), OHG. lecken, legen (MHG., mod.G. legen), ON. legja (Sw. lägga, Da. lægge), Goth. (= OTeut.) lagjan, f. lag- ablaut-variant of OTeut. leg-: see lie v.'
OE = Old English, OFris.= Old Frisian etc.