The full set of Cantigas de Santa Maria survive in four separate manuscripts all dating from the last thirty years of the 13th century. The relation between the manuscripts is complex, with several phases of construction, in each of which new cantigas were added, but the manuscripts were at times being worked on in parallel. All four were subject to later corrections and annotations, sometimes changing them all at once, and at other times correcting some by reference to the others. If you can read Spanish, the Mettmann's introduction (1986) has a discussion of one possible version of the complicated timeline. A subsequent account which found plenty of evidence to disagree with Mettmann is in the following paper:

  The Stemma of the Marian Cantigas: Philological and Musical Evidence
Manuel Pedro Ferreira, 1994

I'll just give some very brief information on each manuscript here for the purposes of identification.

[E] the Escorial "codice princeps" (principal codex, signature j.b.2), held in the Real Biblioteca de San Lorenzo de El Escorial outside Madrid. Also known in Spanish as the códice de los músicos—the musicians' codex—due to the well-known and oft-reproduced miniatures of performers and their instruments that appear before each of the Cantigas de Loor. This is by far the largest of the manuscripts, though modest in decoration compared to [T] and [F]. It contains the prologues and 406 of the cantigas, nine of which are repeated with mostly minor variations, and provides the basis for Mettmann's numbering scheme, which I use on this website.
[T] the Escorial "codice rico" (rich codex), also in the El Escorial library, known as [T] from its manuscript signature T.j.1. Contains the prologues and 195 of the cantigas (originally 203, but eight are missing due to the loss of folios), roughly corresponding to the first half of [E].
[F] the "Florence" codex, now held in the National Central Library of Florence. Contains the text of 104 cantigas, mostly in the second half of [E], but in a completely different order. This manuscript was never finished, and has ruled staves, but no music. Mettmann describes [T] and [F] as "one manuscript in two volumes".
[To] the "Toledo" codex, now in the National Library of Madrid. It includes 129 cantigas, which are apparently amongst the oldest in terms of authorship. Mettmann considered the manuscript itself to be the youngest copy of the four, possibly from the start of the 14th century. Ferreira, on the other hand, considers it to be ‘the oldest surviving source’ from no later than 1280.

An online reproduction of [E] can be found on Greg Lindahl's website, which has black-and-white (not grey-scale) scans of the photographic facsimiles in the edition by Higinio Anglés. These scans are linked directly from each of my individual cantiga pages where available, but if you just want to have a browse around, it will be easier to start from Lindahl's index. For [To], the same site has black-and-white scans from Julián Ribera's book, which I also link to individually.

However, as I mention under Sources in the notes on Using the music transcriptions, the musical notation in Anglés' facsimiles was clumsily retouched by his assistant, and unfortunately the same is true of what Ribera published: his were manually retouched photo-engravings, not photographic facsimiles. So although Lindahl's scans are for the most part very clear and readable, they necessarily preserve occasional misreadings in the original retouching processes. Note also that Ribera's images only include the refrain and first stanza, as underlaid to the music. For genuine full-colour (although not very high-resolution) photographic facsimiles of [To], with the complete text of every cantiga, you can now consult the Biblioteca Digital Hispánica¹ at the BNE; just click on "View work" to see the manuscript.

At present I am not aware of any online facsimiles of [T] or [F], but please let me know if any become available!

[1] It is apparently a condition of linking to that record that ‘Potential users of the content are informed that any use of the images must be expressly authorised, in writing, by the BNE’. It does say elsewhere in their guidelines that downloading for strictly private use is permitted, but anyway, consider yourselves duly informed.