This had once the meaning of earnest, serious, sedate. The passage from Shakespeare quoted below marks ‘sadly’ and ‘sadness’ in their transitional state from the old meaning to the new; Benvolio using ‘sadness’ in the old sense, Romeo pretending to understand him in the new. For the etymology of ‘sad’ see Mayhew-Skeat, Dict. of Middle English.
O dere wif, o gemme of lustyhede,
That were to me so sade, and eke so trewe.
Chaucer, The Manciples Tale.
He may have one year, or two at the most, an ancient and sad matron attending on him.—Sir T. Elyot, The Governor, b. i. c. 6.
For when I thinke how farre this earth doth us divyde,
Alas, mesemes, love throws me down, I fele how that I slide.
But when I think again, Why should I thus mistrust
So sweet a wight, so sad and wise, that is so true and just?
Earl of Surrey, The Faithful Lover, p. 33 (ed. 1717).