c. 1500, "weight, dignity, seriousness, solemnity of deportment or character, importance," from Old French gravité "seriousness, thoughtfulness" (13c.) and directly from Latin gravitatem (nominative gravitas) "weight, heaviness, pressure," from gravis "heavy" (from PIE root *gwere- (1) "heavy"). The scientific sense of "downward acceleration of terrestrial bodies due to gravitation of the Earth" first recorded 1620s.
The words gravity and gravitation have been more or less confounded; but the most careful writers use gravitation for the attracting force, and gravity for the terrestrial phenomenon of weight or downward acceleration which has for its two components the gravitation and the centrifugal force. [Century Dictionary, 1902]
1760, "pertaining to or of the nature of dregs or sediment; precipitated by gravitation from a liquid;" see sediment + -ary. Sedimentary rock in geology is that formed by deposition of material previously suspended in water," attested by 1814.
Sedimental (adj.) "pertaining to dregs" is recorded from c. 1600 and might have lived long enough for a *sedimental journey pun but didn't.