The past tense of hit is hit and the past tense of quit is quit, but to answer why it is the way it is, we need to look at the history.
The verbs quit and hit were not always like that.
Quit is a loan word of French origin.
Most verbs borrowed during Middle and New English attached the dental suffix to mark their PT/PP and thus developed regular forms.¹
So the form quitted for past tense and past participle was widely used in the past.
Only a small number of loan verbs came to be associated with the
surviving types of strong verbs.¹
Hit was one of them and exhibitted "strong" features.
The form "hitten" can be found in archaic texts (from the 16th century onwards).
It might have to do with the fact that it ends in -t.
Phonological factors may have had their share in the selecton of the strong markers. Since [these verbs] contain the stem-final -t/-d/-ð (cf. chide, hide, knit, light, load, put, set, shut, slit, spit, spread, sweat, and wreathe), i.e., the sound which matched the weak PT/PP ending, the selection of the strong marking in Middle and/or New English may reflect an effort to prevent the rise of ambiguous, invariable verbs. But in Present-day English many of [these verbs] (knit, put, set, shut, spread, sweat) selected the non-strong model of tense signalling.¹
It has been shown (cf. Lass 1994) that the past tense and past
participle forms of strong and weak verbs started to become confused
and to interfere with each other as early as the late ME period.
Insecurity in the use of the -en and -ed-suffixes resulted in redundant
suffixations of verbs that were originally weak or had turned weak and
had a stem-final dental fused with the dental suffix (e.g.
knit/knitted, lit/lighted, hit/hitten/hitted, burst/bursten/burtsted;
cf. Sundby, Bjørge, and Haugland 1991:304-313) ²
¹ Language History and Linguistic Modelling: A Festschrift for Jacek Fisiak on his 60th Birthday. Walter de Gruyter, 1997. ISBN 3110820757, 9783110820751
² Rhythmic Grammar: The Influence of Rhythm on Grammatical Variation and Change in English. Walter de Gruyter, 2005. ISBN 3110219263, 9783110219265