The subtle and not so subtle alterations to the basic script of Mark found in the later revisions we call Gospels were made with theological purpose. First century Christians differed on how to understand the lead character, Jesus. A huge percentage held what was later labeled Docetic views of the Christ. He was a spirit that appeared to be human much like angels had done in the OT. As such he always had a perspective that made him somewhat insolated from earthly suffering and weakness. Mark had passages that lent to either a human Jesus or a Docetic one leading later writers and redactors to bring theologically motivated revisions. The eventually prevailing view was that Docetists were wrong. Jesus was completely human. Jesus now had to more explicitly eat and weep and be truly human as well offer other explanations to "clarify" Mark.
G.Luke appears to be the first to have Jesus weep, over Jerusalem in this sole example. The emphasis of his humanity does cause some tension to the G.Mark story. How can he do things like walk on water and appear to be a ghost for example. The writer of G.Luke simply drops that walking on water story as a solution.
How can he be an emanation from God like G.John says and also be given to emotions of human weakness? G.John goes to great pains in crafting his Lazarus resurrection story (probably inspired by Luke 7 and Luke 16 parable) to insist Jesus is not personally grieving for Lazarus but empathetic of those who are. In his mind both elements are vital. (11:4,6,15) That is, above actual sadness but yet compassionate toward the suffering of humans. Interestingly, the Greek words translated as "deeply moved " or "groaned in spirit" in John 11 carry the sense of strong emotion but not necessarily sadness. It otherwise is translated as "stearnly" or "scoldingly" (i.e.. Matt 9:30, Mark 14:5)
It was a theological balancing act, a deity strong and capable but yet empathetic and human.
The newest WT take by one of the speakers (had no desire to watch) likely wasn't intended to be a change in official interpretation but just another effort to sell their religion to grieving listeners.