With reference to Jesus weeping in the Garden- the fact that He cried is only mentioned in scriptures in the book of Hebrews chapter 5 verses 7&8. In the books of Matthew and Mark while in the Garden at that time scripture says He was "troubled", "sorrowful" and "distressed" or "deeply distressed."
I am speaking from the New King James Version, other translations use different words, but to the same effect.
Now, with regard to the account in John chapter 11 where Jesus went to Lazarus several days after he died and said to have wept, the two words used in that account say He was "troubled" and also that he "groaned" in spirit.
Jesus may have cried both times but they were for two different reasons:
From reading all four accounts in the gospel, Jesus is shown to basically feel the weight of the world on His shoulders. He realizes that He must endure great suffering and pain, hence why He asks God the father to remove this cup from Him.
The reason Jesus wept in the book of John is very different. If you read the chapter in its entirety you begin to see a pattern emerging. That pattern is of disbelief of those around Him, especially those spent time with.
I'm not saying it is impossible that Christ cried because he was moved by those crying around Him, or because He loved Lazarus, the context of the chapter in the dialogues that He has with everyone around Him suggest something else.
The word used 8 times in this chapter alone is "believe." Christ raising Lazarus from the dead was to be the climax of His ministry. He was about to raise from the dead someone who already stank in the tomb. There could be no doubt left that He was the Son of God. It was to glorify God (verse 4). No matter who He spoke to, nobody, not even Mary nor His Disciples understood or believed what He was about to do. They did not believe. Hence, this is why Jesus "groaned in spirit" and was "troubled."
The Greek meanings of both of those words means to be agitated or feel alone (troubled) and to be filled with indignation, snort with anger or sigh with chagrin (groaned). This fits with the the theme of unbelief that is present in this chapter prior to Christ raising Lazarus.
"Did I not say to you that if you would believe you would see the glory of God?" (verse 40). Christ used the word "if" to Martha, indicating she did not believe.
Thus I conclude that the reason Christ wept was because He knew what He was about to do (raise Lazarus) but no one would believe.