Last updated: 07-04-2021
A common misconception on the internet is that Sun Wukong’s magic staff was originally used to hold down the Milky Way (fig. 1), suggesting that, since the immortal can effortlessly wield the weapon, he is strong enough to lift the weight of a galaxy. This misconception usually pops up in forums and battle wikis during debates on the lifting strength of particular mythological or fictional characters. It ultimately stems from a mistranslation in the widely read W. J. F. Jenner edition (see the 02-12-23 update for a PDF).  The passage in question reads:
The piece of miraculous iron that anchors the Milky Way in place (emphasis added) has been shining with a lovely rosy glow for the last few days, and creating a most auspicious atmosphere (Wu & Jenner, 1993/2001, p. 55).
However, the original Chinese reads:
我們這海藏中，那一塊天河定底的神珍鐵，這幾日霞光艷艷，瑞氣騰騰… (Wu, 2001, p. 32).
The problem lies in the partial mistranslation of the characters Tianhe dingdi (天河定底). Tianhe is the Chinese name for the Milky Way, while dingdi means to “fix or set the depth or base of.” This refers to setting a fixed measurement for the “Heavenly River” and has nothing to do with anchoring or weighing down anything.
Fig. 1 – A panorama of the top arch of the Milky Way galaxy as seen from Chile (larger version).
The far more accurate Anthony C. Yu translations reads:
Inside our ocean treasury is that piece of rare magic iron by which the depth of the Heavenly River is fixed. These past few days the iron has been glowing with a strange and lovely light (Wu and Yu, 2012, p. 135) (emphasis mine).
Most importantly, the novel is quite clear on how much the staff weighs:
Immediately adjacent to one of the hoops was the inscription, “The Compliant Golden-Hooped Rod. Weight: 17,560 pounds” (Wu and Yu, 2012, p. 135). 
I’ve written a follow up discussing Monkey’s greatest feat of strength.
I have written an article that discusses the magic powers of the staff. These include the ability to shrink and grow, control the ocean, astral project and entangle with Monkey’s spirit, multiply endlessly, pick locks, and transform into various objects. It also has sentience to a certain degree.
Here is my theory on why Sun Wukong’s staff weighs 13,500 catties (Yiwan sanqian wubai jin, 一萬三千五百斤, 17,560 lbs./7,965 kg). I believe the number is an embellishment on the 300 to 500 catty (san wubai jin, 三五百斤) stone block lifted by the bandit Wu Song in the Water Margin (c. 1400).
1) This is the first edition I read as a youngster.
2) Anthony Yu’s (Wu & Yu, 2012) original translation says “thirteen thousand five hundred pounds” (vol. 1, p. 135). However, the Chinese version uses jin (斤), known in English as “catty“. The catty and pound are two different measures of weight, the former being heavier than the latter. Therefore, the English text has been altered to show this. The catty during the Ming Dynasty when the novel was compiled equaled 590 grams (Elvin, 2004, p. 491 n. 133), so 13,500 catties would equal 17,560 lbs.
Elvin, M. (2004). The Retreat of the Elephants: An Environmental History of China. New Haven (Conn.): Yale university press.
Wu, C. & Jenner, W. J. F. (2020). Journey to the West (Vols. 1-4). Beijing: Foreign Languages Press. (Original work published 1993)
Wu, C., & Yu, A. C. (2012). The Journey to the West (Vol. 1) (Rev. ed.). Chicago, Illinois: University of Chicago Press.