All four of these categories are important. The hierarchy of significance is flexible, so the researcher has to be careful. It is possible that one category alone can determine the answer, however, best is that all should be considered. Clearly, in practice there will be some overlap, with one category giving input to another.
1) Physical Evidence (primarily the condition of the parchment, ink and binding, without regard to the actual words or pictures)
"a document is no older than the materials used"
A book made from a type of material that was only created in 1800, the book cannot be older.
Material testing has come up as a primary resource in exposing various forgeries. (However, at times the science is contestable, partly because control testing of neutral manuscripts is not common, partly because of issues like contamination.) Usually the testing is done after other issues, like history and provenance, or a text too good to be true, raise questions.
As an extreme, if a book is in "proof" condition, then it can not have endured heavy use over centuries. (The CFA has this concern)
And there can be special physical evidences, like the colour distinction of Leipzig and British Library, that points to historical tampering. Thus, a Physical and Historical combined evidence.
With Sinaiticus the "exceptional" physical condition does not fit the vulgate version of its history. A manuscript coming from 350 AD and having hard use till the medieval era and then more hundreds of years of storage and/or light use should show grime, wear and fatigue (brittleness) far beyond either section does today.
2) Palaeographic Evidence
Most significantly, the handwriting. What era wrote in that style?
"That is the way they wrote in 500 AD"
Related disciplines that can be considered here include Codicology
"They made books that way in 550 AD"
Sinaiticus was dated by Tischendorf mostly by palaeographic evidence, ignoring the time symmetry element, along with some textual elements, including the missing ending of Mark. Later writings all around the base text were simply assigned to various centuries. In general, those assignments of Greek and Arabic writing have gotten little review, and the actual Arabic claims have been wildly divergent. With Sinaiticus, we have an unusual situation: if there were weird palaeographic anomalies in the base text, there were many years of unprovenanced and suspicious activity, private time, where sheets could be discarded or modified.
Note on Time Element Non-Symmetry
Note that many aspects of Physical and all aspects of Palaeographical are, in terms of a time scale, non-symmetrical. ie. They are much more helpful in the terminus post quem than the terminus ante quem. They tell you quite well the earliest date it is written, but usually leave open the latest date to a wide range. (Brent Nongbri has pointed this out in papyri dating, the range of dates is far too limited.) This is putting aside cases where external documentation can "fix" the date.
A person in 300 AD cannot write in a script style that only began to be used in 700 AD. Yet a person in 700 AD can still be writing in the "old style". He may respect the style and keep it in his writing (on this basis any of the uncials could easily be much later than their palaeographic determination, a point emphasized by P. C. Sense, Michaelis and others.) Or the style may have simply lived on in certain environments. A church environment may keep an old style script deliberately (An example is Old Church Slavonic.)
And, those doing replicas and forgeries will deliberately write in the old style. So seeing a script style, by itself, is a piece of information that has value, but that value is limited, and all the elements of dating must be considered.
Once a material or writing style exists, it can be used or copied at any time as an unexpected continuation of the style, or even simply for play by the scribe, or for a replica, or for forgery. One of the major errors in modern dating is to try to use palaeography to straight-jacket a date (e.g. a papyrus is given as from 200-250 AD when the true range would be 200-550, even if it is considered likely that it is 3rd century.)
3) History and Provenance
This includes all the historical elements around a manuscript. How and where is it discovered. What is its history.
This includes external evidences (external to the text.) E.g. A manuscript might be found with a laundry list that, if authentic, is clearly from 550 AD. Or internally the ms. may simply give the necessary information. (Codex Fuldensis is a good example, although even there you have to remember the non-symmetry aspect, the full ms. could be copied 200 years later with the same names given.) Thus, when there are external evidences, it can "fix" or corroborate the palaeographic. On the other hand, when the provenance of an item is shaky, then recent replica or forgery production must be considered, and the physical evidence becomes paramount, sometimes along with auxiliary questions like dependencies.
Historical and provenance are a widely diverse area, later we may try to do an a-b-c . This came up a lot on issues like exposing Archaic Mark as a forgery. Sinaiticus has a very special type of independent evidentiary corroboration, where the specific historical claim of tampering by colouring was not checked at the time, but was easily confirmed after 2009!
4) Textual probabilities and dependencies
Looking at the actual text may give weak or strong hints as to when it was created. This can be the text-type, individual variants, groups of variants, and things like section numbers.
Dependencies show that one ms. was, apparently, using another ms. With ms. 2427 this was a key item, the evidence was extremely strong that it was made using an 1800s printed edition. Research on possible dependencies involving Sinaiticus is ongoing.
With Sinaiticus (2) palaeography, has been the base of the dating. When there was some challenge to this dating, (4) textual, was an important support. (1) physical and (3) historical, provenance were largely ignored, or skewed. A good exercise would be to see how Sinaiticus has worked with all four evidences. Similarly, to take a number of particularly mss, (e.g. a papyrus that has an external dating, Alexandrinus, and 2427) and discuss which features are really important in determining both dating and authenticity.
Now, let us discuss an evidence that is a hybrid of the two categories.
The colouring of Sinaiticus between Leipzig, 1844 and the deposit of the St. Petersburg leaves in 1862, most likely in Sinai in the 1850s, possibly augmented in Cairo in 1859, is, upon examination, a simple historical fact. We can agree that it would be helpful to actually test the manuscript, but the owners of the mss seem to be somewhat reluctant to have this done. Leipzig was reported at one point to have planned testing, and then pulled back, circling the horses.
So the colouring of the ms is both a physical materials evidence (aided by The Tale of Two Manuscripts) AND an historical/provenance issue (consider e.g. the 1863 publications of the accusation that this colouring had been done) combined.
On the other hand, the general "exceptional", youthful, flexible, supple condition of the manuscript is simply a physical evidence. So we should be aware when an evidence is in one category, or combined categories.