Sorry, I just reedited my previous comment. So my question is on 3 nights. 3 days is fine.
So Friday night is 1 night, Saturday night is 2 nights. He did spend third night! So it's 2 nights only and not 3 nights!
A little more digging, and it seems to the people and idiom of the day it was not strange.
"For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth." - Matthew 12:40
De Trin., iv. 6: For that the three days were not three full and entire days, Scripture witnesses; the first day is reckoned because the latter end of itcomes in; and the third day is likewise reckoned, because the first part of itis included; while the day between, that is the second day, appears in all its twenty-four hours, twelve of the night and twelve of the day. For the succeeding night up to the dawn when the Lord’s resurrection was made known, belongs to the third day. For as the first days of creation were, because of man's coming fall, computed from morning to night; so these days are because of man's restoration computed from night to morning.
- Augustine of Hippo
(Born in the 300s)
"For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth." - Matthew 12:40
Christ says he will spend “three days and three nights in the heart of the earth.” He is referring to the end of Friday, all of Saturday and the beginning of Sunday [of the passion week], in keeping with the way people understood the beginning and ending of days. For we too commemorate the third day of those who have died, not when three days and three nights, completed in equal measure, have gone by. But we reckon as a single, complete day that day on which the person died, regardless of what hour the death occurred. We count as another day that on which we take our leave of the departed in hymns before the tombs. Following this same kind of sequence, then, the Lord announced that he would spend a full three days and nights under the earth. A clear indication of this is the fact that the women arrived at that very time, in order to fulfill those things that the law prescribed to be done for the dead upon the third day.
- Theodore the Stratelates
"For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth." - Matthew 12:40
He calls them an evil generation as they were deceiving tempters, and adulterous, because they had abandoned God and followed after demons. He calls His Resurrection a sign as it is marvelous beyond belief. For having descended into the heart of the earth, the nethermost part, which is hades, He arose on the third day. The three days and three nights you must understand as spoken of in part and not in their entirety. For He died on Friday, which is one day. He was dead on Saturday — behold, the second day. And the night of Sunday held Him still dead. The three days and nights, then, are counted by parts, in just the same way as we often count them ourselves.
- Theophylact of Ochrid