From BiblePortal Wikipedia

King James Dictionary [1]

Sad, a. It is probable this word is from the root of set. I have not found the word is from the root of set. I have not found the word in the English sense, in any other language.

1. Sorrowful affected with grief cast down with affliction.

Th' angelic guards ascended, mute and sad.

Sad for their loss, but joyful of our life.

2. Habitually melancholy gloomy not gay or cheerful.

See in her cell sad Eloisa spread.

3. Downcast gloomy having the external appearance of sorrow as a sad countenance.  Matthew 6 . 4. Serious grave not gay, light or volatile.

Lady Catherine, a sad and religious woman.

5. Afflictive calamitous causing sorrow as a sad accident a sad misfortune. 6. Dark colored.

Woad or wade is used by the dyers to lay the foundation of all sad colors.

This sense is, I believe, entirely obsolete.

7. Bad vexatious as a sad husband. Colloquial. 8. Heavy weighty ponderous.

With that his hand more sad than lump of lead. Obs.

9. Close firm cohesive opposed to light or friable.

Chalky lands are naturally cold and sad. Obs.

The two latter senses indicate that the primary sense is set, fixed.

Webster's Dictionary [2]

(1): ( supperl.) Sated; satisfied; weary; tired.

(2): ( supperl.) Heavy; weighty; ponderous; close; hard.

(3): ( supperl.) Dull; grave; dark; somber; - said of colors.

(4): ( supperl.) Serious; grave; sober; steadfast; not light or frivolous.

(5): ( supperl.) Affected with grief or unhappiness; cast down with affliction; downcast; gloomy; mournful.

(6): ( supperl.) Afflictive; calamitous; causing sorrow; as, a sad accident; a sad misfortune.

(7): ( supperl.) Hence, bad; naughty; troublesome; wicked.

(8): ( v. t.) To make sorrowful; to sadden.