The phrase to pull one’s weight means: to do one’s fair share of work.

 

ORIGIN

 

The verb to pull is used to mean to pull on an oar or oars so as to move a boat, to row; for example, in The Early History of Oxford, as published in Macmillan’s Magazine (London and Cambridge) of October 1871, the English historian John Richard Green (1837-83) wrote:

Royal recognition enables us to trace the merchant guild of Oxford from the time of Henry I.; lands, islands, pastures already belonged to it, and amongst them the same “Port-meadow” or “Town-mead” so familiar to Oxford men pulling lazily on a summer’s noon to Godstow, which still belongs to the freemen of the town.

Cooperation between rowers is required; in A Treatise of Human Nature: being an attempt to introduce the experimental method of reasoning into moral subjects (London, 1739-40), the Scottish philosopher and historian David Hume (1711-76) wrote, about a general sense of common interest inducing all the members of the society to regulate their conduct by certain rules:

When this common sense of interest is mutually expressed, and is known to both, it produces a suitable resolution and behaviour. And this may properly enough be called a convention or agreement betwixt us, though without the interposition of a promise; since the actions of each of us have a reference to those of the other, and are performed upon the supposition that something is to be performed on the other part. Two men, who pull the oars of a boat, do it by an agreement or convention, though they have never given promises to each other.

The literal meaning of to pull one’s weight is to row with effect in proportion to one’s weight; for instance, the following is from The Daily Telegraph (London) of Thursday 18^th March 1869:

Dark Blue against Light Blue ¹. The race will be pulled to-night; the start is from Westminster Bridge. The odds are ten to one on the dark colour, and there are no takers. The Light Blues have been for years past knocked out of shape and form—save two years ago, when Lowe caught that crab ²,  and Disraeli took the Dark Blues’ water; and they are beaten before they step into their boat. Just look at the men; can there be a doubt as to the event? There is, as Stroke of the Dark Blues, Gladstone, of Christ Church; surely he can pull a trifle. We have seen him at work many a time, with his long, sweeping action—and what a biceps! That man is always in condition; he never wants physic, or flannel shirts, or “breathers;” why, he would pull the boat through in his sleep. Then Jack Bright: there’s an oar for you! See what comes of letting Dissenters into the University. A shade heavy he may be; but he pulls his weight many times over. So tremendous, indeed, is his muscle, that, if he were to lash out, he would pull the University eight right under water; but he won’t.

¹ Dark Blue refers to the shade of blue adopted by Oxford University as its colour, Light Blue to that adopted by Cambridge University.
² To catch a crab means to make a faulty stroke in which the oar is jammed under water or misses the water altogether.

As B. A. Phythian explains in A Concise Dictionary of Phrase and Fable (1993):

If one member of the crew does not pull the oar with a force appropriate to his or her weight, the rower then fails to make the contribution expected by the rest of the crew.

The earliest figurative use of the phrase that I have found is from The Daily News (London) of Wednesday 10^th February 1897:

THE NEW MEREDITH ³.
“Evan Harrington.”

In noticing the extensive alterations made by Mr. George Meredith in the text of “The Ordeal of Richard Feverel” for Messrs. Constable’s new edition, we predicted that when “Evan Harrington” appeared it also would be found to have undergone somewhat drastic pruning. Those who have read “Evan Harrington” as it came out thirty-seven years ago […] are aware that the text of the later editions has been greatly altered. […]
One cannot but regret much of what is gone. Jack Raikes was a caricature, of course; he was drawn in the manner of Dickens, and he was entirely impossible. But we never found him tedious. In boating phraseology, he “pulled his weight” in the tale; he was not a mere passenger.

³ George Meredith (1828-1909) was an English novelist and poet.