John 11:35 Jesus wept. This is arguably the shortest verse in the Bible. It records the anguish of the Lord over the sorrow of his friends at the death of Lazarus.
Another incident is recorded in Luke 19:41 when, regarding Jerusalem from afar, Jesus wept over it knowing what would befall the inhabitants of the city because of their rejection of him.
The bottom line answer to your question is that it is specifically recorded twice that the Lord wept.
However, consider Hebrews 5:7,8 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; Though he were a Son, yet learned he obedience by the things which he suffered
The Lord was no stranger to tears. In his successful struggle against the power of sin, his prayers were of such intensity and passion that they were frequently accompanied by tears. Isaiah 53:3 tells us that the suffering Messiah would be a man of sorrows, and acquainted with grief. So, to my mind, tears would have been a constant companion during the years of his ministry.
So the real answer is Jesus wept in private frequently although only two instances of public weeping are recorded.