In TB weddings the groom tries to walk off to Kasi.
Bride's father tells him to come back and marry his daughter.
After some photos the boy readily agrees and then the groom and bride exchange garlands.
Is there a deep significance to this function?
Does it have a basis in Vedas?
Yes it does have some significance -- whether the significance is deep or shallow depends on how we view it.
The snAtakA (the student who returns from Gurukulam after the ceremonial bath) returns to his parents after studies. He is still impressed by the vairAgyam (renunciation) spirit that has been drummed into his head by the study of upaniSads etc. and wants to retire to the forest to pursue his "Atma vidyA". Initially the parents of the boy are impressed with his determination and give him walking stick, umbrella etc. for his proposed sojourn to the deep woods.
But then it dawns on them that mOksha may not be possible unless he passes through the four Ashramas and he has to pass through the grhastAshram before his mind mellows and attains the maturity to have the requisite vairAgyam and the parents of the boy themselves may never escape the cycle of birth and death, unless their son performs antyeshti (last rites) for the parents and performs at least the first SrAddham (when the parted soul is supposed to join other souls of the same lineage or sayyujyam with their Lord (or stay in heaven/hell etc.)
So he is called back and persuaded to be a gruhastA and raise a family to ensure "vamsha vruddhi" and they also say that they have identified/selected a good "kanyA" as his bride. The boy (or groom) relents and agrees to be a gruhastA and he would pursue his life journey of vAnasprasthAshrama later. The vAnasprasthAshrama will ideally commence after he has had a look at his grandson and he will lead his further life in forests subsisting on leaves and roots and water from the streams etc. making him superfluous on this earth and focus on AtmavidyA.
As you can see from the above, the arranged marriage, staying with the parents till they depart to the other world or take to vAnaprasthA are rather deeply ingrained in a Hindu psyche and thats why you will find resistence from conservatives or oldies to the changes which "liberals" try to thrust upon them with the idea of love marriage etc. through forum such as ours.
Initially the exchange of garlands in itself signified marriage and there was a sumptuous meal to solemnise the event. But thereafter many other rites have also been added (which also have quite a significance).
About photos, well I am sure you know the modern saying "marriage is temporary, but photos are permanent".
The reply would be incomplete without making a mention of modern day spin that the groom is tempted wih the offer of a beautiful bride, temptation is hard to resist (and examples of vishwAmitra, mAneka etc. are thrown in).
About whether it has a basis in vedAs, I think yes. I remember reading or hearing someone say it is there in Araynaka, most probably in taittiriya AraNyakam. But I would like you to take this as just my "opinion". If you really need it, I will have to make a lot of searching.
The knowledge about Dharma is scattered in the four vedAs and in the four components of vedA viz. samhita, brAhmaNam, Aranyakam and upaniSad and it would be like searching for a needle in haystack. To cut short this lengthy search, our forefathers had made a compilation called "Dharmasindhu" which distills the dos and donts for a conservative Hindu. I think dharmasindhu in various languages is freely available in the net and the book form is not too costly either.