Paul signs this letter in verse 11 and it is likely that the rest of the letter was written by Paul himself. Letter-writing was normally done through a secretary, an amanuensis. The secretary may have had some freedom to express the thoughts of the author in better language than was originally dictated. It was common practice for the author of the letter to add a personal greeting at the end of the letter. Perhaps this adds a personal touch to the letter, but it might very well signify approval of the contents of the letter. This is something like a busy executive having a his secretary draft a letter then adding a personal greeting by hand at the end.
Witherington (Galatians, 440) cites P.Oxy 265 as an example of a concluding note added to a document. If you following the link to you can see a photograph of this practice of adding to the end of a document. (Even if it is “all Greek to you,” look at the document, you can clearly see the larger handwriting at the bottom of the contract.) This document is a wedding contract, written during the reign of Domitian (A.D. 81-96). After 37 lines of regular handwriting, a second hand adds several lines, and a third adds the final three lines in much larger handwriting. It is hard to make much sense of these lines since they are fragmentary, but the last two lines includes the words “my husband” and “by her in my name.” Perhaps the first hand is from the father, the second is form the mother. These brief additions (threats?) to the end of a marriage contract are in their “own handwriting.”
What does “large letters” mean? The Greek word (πηλίκος) can indicate the importance of something or even the length of the letter itself. The phrase might mean something like “look at the length of this letter!” The noun gramma (γράμμα), “the letters” (dative plural) indicates the means by which Paul was now writing, with larger handwriting. Like the P.Oxy 265, the original copy of the letter to the Galatians included this conclusion personally written by Paul. It was noticeably different than the rest of the letter, and gave a personal touch to a rather contentious letter.
Why write in large letters? Zeisler thought this meant that the reader of the letter should turn the letter to the audience so that they could literally see the words Paul was writing (Galatians, 98). It is also possible these large letters indicates emphasis, the “ancient version of bold print” (Witherington, Galatians, 441). While either of these is a possibility, the most common suggestion is that the largeness of the letters was due (in part) to Paul’s poor eyesight. Galatians 4:15 seems to indicate that Paul had some sort of eye trouble, perhaps he still struggles to see clearly and simply wrote in a larger hand because he was not able to see very well.
In the light of the papyri fragment above, this reference to large letters may simply indicate that Paul was following normal contemporary letter-writing practice by finishing the letter himself, adding a final word to sum up the whole letter.