Why are "said" and "paid"/"laid" pronounced differently?

The words say, pay, lay are phonemically /seɪ/, /peɪ/ and /leɪ/ respectively (with the diphthong /eɪ/). Their past and past participles are respectively: /sɛd/ (or /sed/), /peɪd/ and /leɪd/. The past/past participle (and present simple singular) of "said" contains a vowel instead of the expected diphthong /eɪ/.

Say and lay are both Old English words while pay is from Old French through Middle English. "Say" and "lay" belonged to the same verb class in Old English, if I understand it correctly. That’s why their past/past participle are spelled the same.

I didn’t have much luck tracing their roots and finding what happened that caused "said" to have the vowel /ɛ/ instead of the diphthong /eɪ/.

So why does "said" have a vowel and not a diphthong?