The term "up to my eyeballs" is used when someone is saying that they have had enough or have had so much of something that they are about full. An example is, "I have been up to my eyeballs in work lately." Meaning a lot of work. It is an exaggerated term.
He wanted people to think he knows what he is talking about, but everyone knew he is full of hot air. Someone who is full of hot air talks a lot, but they are not knowledgeable about what they are talking about.