The chief current uses, that is orderly, neat, etc. are on record only from the opening years of the eighteenth century, and earlier meanings are: timely, in good condition, well-favoured, of good character.
Ultimately ‘tilt’ has its origin in a word that meant to overthrow or overturn, made familiar to us by scenes of combat in which mounted knights sought to unhorse their opponents. In iron working it was the name given to a heavy hammer used in forges: this was fixed on a pivot and acted upon by a cam-wheel which alternately tilted the hammer up and then let it drop (OED).
A word which goes back to Old English with no real change in meaning. These were the tools which made the moving and handling of heated iron possible and in most smithies there would be a range of such implements: they were an essential part of ‘smithy gear’.