Drawback is formed from the verb draw, meaning to pull, and the adverb back. The verb form meaning to retreat or recoil was indeed around since about 1400, according to the Oxford English Dictionary, and there's a nonce usage in noun form in 1619 that I haven't been able to duplicate in "drawback, n. and adj.":
1619 E. M. Bolton tr. Florus Rom. Hist. ii. vi. 151 Fabius..got the nick-name, to bee called, The draw-backe, or Cunctator.
In effect, a draw-back cunctates or delays work.
The noun form comes more fully into English as a nominalization of a trade policy whereby import duties would be paid back on goods subsequently exported. The verb for a trader drawing back (taking back or receiving back) the duty payments they received was quickly nominalized.
Here is a 1699 source, "An Account of rock-salt from the 25th of Decemb. 1699, to the 25th of Decemb. 1700," that shows both the noun form and the verb form together.
Rock Exported, part of the Sum above, which Duty was all drawn back and discharged by so much of the first Bonds given for the Rock.
Which Duty was discharged by the Draw|back allowed, and satisfied by so many of the first Bonds given for the Rock.
Rock Rest as Ballance at the Works, -- for which the Bonds are out and will be discharged if the Rock shall be melted, by the Draw-back, otherwise must be paid.
This drawback policy came with one of the Navigation Acts passed in the 17th century to regulate trade policies. I'm not a legal expert, but a parliamentary law passed in 1695-6 allows for drawbacks for salt:
That all Salt made from Rock Salt (allowing the Draw-back for the same as in the said Act is mentioned) ...
This usage saturates the 2000+ results in the Eighteenth Century Collections Online database, with many mentions in histories, recorded debates of Parliament, and other sources.
The first usage cited in the Oxford English Dictionary for a meaning like "hindrance" seems to play off of this commercial meaning. Here's an excerpt from The humourist: being essays upon several subjects (1720):
I am apt to think that every new Acquisition of Power, Wealth, or Fame, gives a new Touch and Bias to the Imagination. Ever since I began to be an Author, I have taken up an uncommon Passion for wearing of Ruffles; but, to shew how much the Philosopher in me gets the better of the proud Man, I have, at the same Time, as a Drawback upon my Ambition, laid aside my Silver Buckles, and contented myself with humble Bath-Metal.
The action of laying aside silver buckles acts as a way to restrain his ambition. The strict economic sense is stretched: he may be paying back one behavior for having previously acquired ambition in another, ruffled form. By the time literary author Samuel Richardson writes Clarissa, the meaning of disadvantage is clearer:
1747 S. Richardson Clarissa I. xiii. 73 Daughters were but incumbrances and drawbacks upon a family.
To the aspirational English patriarch in the 18th century, daughters require paying out wealth, constituting a drawback on family fortunes unless they comply with a patriarch's wishes and marry well.