It is certainly puzzling, and not only to you. The problem has frustrated many scholars and is thus described on page 724 of The Nordic Languages: An International Handbook of the History of the North Germanic Languages by Bandle et al. (dealing with the disappearance of the dental stop in the third person singular – and its replacement by -ʀ → -r):
Concerning the apparent addition of -t in the second person singular, a similar (or, indeed, the same) development also takes place in West Germanic, as is known from German and older stages of English (e.g. "thou knowest", "thou dost" in the language of Shakespeare and the KJV). The common explanation that it results from a rebracketing of cases where the verb is immediately followed by the second person singular pronoun is rejected by Ringe & Taylor in their 2014 The Development of Old English (pp. 253–254):
In the following he instead gives a somewhat complicated and lengthy account of an alternative theory, the gist of which is expressed below (ibid.):
As they note, this development must have occurred later than the Proto-West-Germanic stage, and thus does not per se account for the system seen in North Germanic, but it is perhaps not inconceivable that the general principles in the development spread via a wave model also to the North Germanic languages.