إِنَّ أَوَّلَ بَيْتٍ وُضِعَ لِلنَّاسِ لَلَّذِي بِبَكَّةَ مُبَارَكًا وَهُدًى لِلْعَالَمِينَ
The root fo the word بِبَكَّةَ used in 3:96 of the Quran is ب ك ك which has the following meanings:
crowding together of people; lacking water; and breaking of the neck.
These meanings are all associated with Mecca as this is where (1) people crowd together for Hajj, (2) aside from occasional rains that cause floods it is a desert and lacks water (3) anyone who attempts to lay siege on the Kaaba is not successful and thus breaks their neck e.g. The People of The Elephant.
Some have the false understanding the the word بِبَكَّةَ comes from the same word as “to weep”. This misunderstanding appears to have originated from the Greek translation of Hebrew of Psalms 84, where the early Greek translators translated the Hebrew word Bakka בכא (ba-k-a) which is a name to the similar-sounding word בכה (be-k-ha) which means “crying or weeping” and translated the mention of “valley of Bakka” in Psaml 84:6 as: ἐν τῇ κοιλάδι τοῦ κλαυθμῶνος “valley of mourning or weeping”. This is an inaccuate translaiton as בכא (ba-k-a) & בכה (be-k-ha) are two completely different words despite sounding similar.
Similarly, in Arabic the word for weeping is بَكَى (ba-ka-ya) which is pronounced as baka, but again is a completely different word than بَكَّةَ (bakka) which is the name Bakka, the ancient name of Mecca.
To put this in perspective for English speakers, this would be equivalent to translating the word “blew” as the color “blue”. Despite sounding the same these words are fundamentally different.
If you are interested to know why God might have used two names for the same location then check out the following article