"And he moved from there to the mountain on the east side of Beis-El and pitched His/Her tent" (Bereishis 12:8)
Rashi from Beraishis Rabbah 39:15 states that the vowels in the word Ohelo/his tent are written so that the word is pronounced Ohelah/her tent. This tells us that Avrohom put up Soroh’s tent before his own. This was because he wanted to honor her more than himself (see Gemara Yevamos 62a).
It is important to note that Avrohom and Soroh were not on shidduch dating anymore. They had been married many years and they still acted with respect and formality with each other. One must never stop showing Kavod to his wife.
The Mattenos Kehunah says that Avrohom was concerned for her Tznius as it says in Tehillim 45:14 "All of the king's daughter’s Kavod is in the palace". He may be saying that this was an additional factor because if her going into a tent was only for modesty she could have gone into any tent (see 18:19, where she is praised as a Tzenuah for being in the tent, but not "Ohela – her tent").
Still, why is it necessary to add the factor of Tznius to what the Medrash said?...
Isn’t it enough that he put up the tent to show her honor?
We see that Tznius is a part of Kavod. In addition to all the other reasons for a man or woman to act modestly it is also showing Kavod for themselves or self-respect.