The verb "to fit" can be used with a direct object (e.g. to fit a new gearbox in a car) or without (e.g. to fit in a suitcase).
"Fit" and "fitted" are both proper past tenses for the verb "fit".
In American English perhaps but not in British English, where "fitted" is the only correct past form, whether or not the verb has a direct object. Thus -
"I fitted a new gearbox"
"My clothes fitted in my suitcase".
"Did fit" is grammatically correct, but it is emphatic. You would only use it if there had previously been some doubt, e.g. -
"I had feared that I had too many clothes for my suitcase but they did fit".