Why was Principia Proposition 43, Theorem 22 not published?

Question

Why was Proposition 43, Theorem 22, of Newton's Principia not printed?

Weinberg, To Explain the World (2015) describes this proposition:

In an unpublished “Proposition 43” that did not make it into the Principia [why?], Newton acknowledged that Tycho’s theory could be true if some other force besides ordinary gravitation acted on the Sun and planets.²²

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^{22. G[eorge]. E. Smith [of Tufts University], to be published.}

It appears on MSS add. 3965, fol. 341r:

Transcription (Sungenis 2018 p. 407n470):

Ut Terra quiescat in centro Systematis Solis Planetarum & Cometarum, requiritur et gravitas universalis, et alia insuper vis quæ agit in omnia coropora æqualiter pro quantitate materiæ in ipsis et æqualis est gravitati acceleratrici qua Terra tendit in Solem, eique contraria est, tendendo secundum lineas parallelas in plagam eandem cum linea quæ ducitur a centro Solis ad centrum Terræ…Nam talis vis in corpora omnia æqualiter & secundum lineas parallelas agendo situm eorum inter se non mutat sed sinit corpora eodem modo per vim gravitatis universalis inter se moveri, ac si non ageret in eadem. Terra vero, cum hæc vis gravitati ejus in Solem æqualis sit & contraria, in æquilibrio inter has duas vires manere potest et quiescere. Et sic corpora cælestia circa Terram quiescentem moveri possunt ut in Systemate Tychonico.

English translation:

In order for the Earth to be at rest in the center of the system of the Sun, Planets, and Comets, there is required both universal gravity and another force in addition that acts on all bodies equally according to the quantity of matter in each of them and is equal and opposite to the accelerative gravity with which the Earth tends to the Sun. For, such a force, acting on all bodies equally and along parallel lines, does not change their position among themselves, and permits bodies to move among themselves through the force of universal gravity in the same way as if it were not acting on them. Since this force is equal and opposite to its gravity toward the Sun, the Earth can truly remain in equilibrium between these two forces and be at rest. And thus celestial bodies can move around the Earth at rest, as in the Tychonic system.

Answer 1

Final edition has both Proposition 43 and Theorem 22 (in book 1) but they are different from what you cite. Book 3 contains only 42 propositions.

Of course we cannot penetrate Newton's mind, so this is a question of opinion. On my opinion, at the time of Newton nobody considered Brahe's system seriously (it became obsolete after the discovery of Kepler's laws).