The pronunciation of the vowel sounds in many English words underwent changes between 1200 and 1600 in what's known as the Great Vowel Shift. Many words that had been pronounced with what we call a "short e" (as in "bed") came to be pronounced with a "long e" (as in "bead"). Prior to then, in Old English and Middle English times, the verbs sleep, keep, weep, and sweep were pronounced more like slep, kep, wep, and swep. The past tenses were not really all that irregular. They were formed by adding the unvoiced "t" sound instead of the voiced "d" sound simply because it's easier to say "t" after "ep" than to say "d".

As to why the present tenses of these verbs underwent the vowel shift while their past tenses kept the older pronunciations is something I'm not boring jadrool enough to know.