Why So Pale and Wan

The piece itself is a lyrical poem.

Mr. Sir helpfully tells us that this song is from the play 'Aglaura', and that directly preceding this song comes a line from the character Orsames:

'A little foolish counsel... I gave to a friend of mine... when he was falling into a consumption.'

Why call it a 'consumption'?  It's actually an archaic term for tuberculosis!

(Extract from the above link)-

The much older name originally came from the ancient Greeks who called the disease something meaning “consumption,” “phthisis,” specifically referring to pulmonary tuberculosis, with the earliest references to this being in 460 BC.

The “father of Western medicine,” Hippocrates, estimated that phthisis was the most widespread disease of his age. He further told his students that they shouldn’t attempt to treat patients in the last stages of phthisis, as they were sure to die and it would ruin his protégés’ reputation as healers if they made a practice of attempting to heal such individuals.

Tuberculosis wasn’t just found across the pond either, but it is known to have been present in the Americas as early as 100 AD.

So why was “phthisis” aka “consumption” chosen for the name? It was because the disease seemed to consume the individual, with their weight drastically dropping as the disease progressed.

The author, Sir John Suckling, was also a Cavalier.  So he was of the English gentry and was a royalist supporter of King Charles I in the English Civil War. (In that last link, it's all interesting, though the most relevant bit is possibly the 'Class Divisions' section about halfway down.)

Wikipedia also provides us with further information on both the poet and his play, Aglaura.

As a dramatist Suckling is noteworthy as having applied to regular drama the accessories already used in the production of masques. His Aglaura (pr. 1638) was produced at his own expense with elaborate scenery. Even the lace on the actors' coats was of real gold and silver. The play, in spite of its felicity of diction, lacks dramatic interest, and the criticism of Richard Flecknoe (Short Discourse of the English Stage), that it seemed "full of flowers, but rather stuck in than growing there," is not altogether unjustified.

On a related note, the decisive (and derisive!) tone of the final line may also give us some insight into the character of the author, as Wikipedia further tells us

"In 1639, Suckling assisted King Charles I in his first Scottish war. Putnam's Monthly Magazine of American Literature states,

At the breaking out of disturbances in 1639, when the Scottish Covenanters advanced to the English borders, many of the courtiers complimented the king, by raising forces at their own expense. Among these, none was more distinguished than Sir John Suckling. These gallant gentlemen vied with each other in the costly equipment of their forces, which led the king facetiously to remark, that "the Scots would fight stoutly, if only for the Englishmen's fine clothes." The troop of horse raised by Sir John alone cost him, so richly was it accoutred, twelve thousand pounds. In the action which ensued, the sturdy Scots were more than a match for the showy Englishmen; and among those who particularly distinguished themselves by their shabby behavior, was the splendid troop of Sir John Suckling. There is every reason to believe that Sir John personally acquitted himself as became a soldier and a gentleman; but the event gave rise to [a] humorous pasquil, which, while some suppose it to have been written by Sir John Mennis, a contemporary wit, others have attributed to Suckling himself."

Hope this helps.  I recommend you do your own further research!

- T. Marcus