Hello @ZenNudist - happy to explore it a little, but probably won't go into too much depth here so as not to derail things too much for the OP :) It is a really interesting area, though. It's always so important to remember how people living in C1 Palestine would have heard the words Jesus said, and also how they would have interpreted his actions. He made explicit and implicit claims to divinity (and not just any divinity, but to the God of the Jews, the God these people worshipped).
When he went round healing people, he was making an implicit claim, but he so often went further by claiming to have authority to forgive sin and to exorcise demons - his audience would have believed only God has authority to do this, so would have recognised that Jesus was claiming to be one with God. He also made claims about himself which were both resonant and consistent with OT theology and scripture, especially the 'I am' sayings - The use of I am would have been particularly inflammatory because of the way he used it - not only in the 'I am the Light of the world' etc but in his use of 'before Abraham was, I am' in John 8 - using present tense to represent the fact he is eternal, and also referring to the name the Israelites knew God as - Yahweh, recalling God speaking to moses in the burning bush. because of this the crowd tried to stone Jesus - they thought his words to be blasphemy because they were so obviously claims to divinity.
In addition to this, Jesus made direct claims calling himself the Son of God and Son of Man. It's often argued these were merely ways of expressing an affinity with the Jews as children of God, but in actuality these were well-known messianic claims. Son of Man was an expression used in the OT book of Daniel when Daniel had a vision of God on the throne of heaven, so by using this name the audience would have been left in little doubt that Jesus was claiming to be not only the messiah but God himself.
He also answered questions pertaining to his status as son of God in the affirmative. His statements throughout the gospels reveal that he had this self-understanding from early on, right through his ministry - from his visit to the temple as a boy through to his statment in John 3:16 that God so loved the world that he sent his only son. He also uses parables to make claims that he is the son of God, for example the parable of the vineyard owner in Mark 12 - he speaks here of the son as revered above prophets. He also received worship without rebuking the worshippers.
We see so many times from the response of the people and especially the authorities that Jesus was making claims above and beyond being a child or prophet of God. That, his use of explicity messianic language, his use of parables, his actions and outright claims all point towards a self-understanding as both human and divine, as the son of the Father who came into the world to reconcile the world through his death and resurrection.
Sorry - have wittered a little.