What Does “Jesus Loves Me” Mean?

David Heddle doesn't like philosophy. About proofs of theistic claims, he says:

I don't even like the proofs of God from Aquinas and Anselm. I prefer: Jesus loves me this I know, for the bible tells me so. [italics in original - MJH]

Christians often say "I know Jesus loves me." They say it as if it were perfectly obvious, but I don't what it means.

The statement is identical in form to the statement that "I know my wife loves me." But I do know what that means: my wife is here with me, right now, in our home. She's a living person, and she actually tells me she loves me. If I am in doubt, I can simply ask her.

Heddle's statement is also identical in form to "I know Julius Caesar loves me." What meaning should one assign to this sentence? Caesar lived in Rome, around 2000 years ago. I live in Albany, in the present. He didn't know me then (because I wasn't born yet), nor does he know me now (because he's not living anymore). Why speak of him in the present tense? If the statement "Julius Caesar loves me" is read literally, then the statement is either false or meaningless.

So in one case, we have a statement that is meaningful and true, and in another case we have a statement that is either meaningless or false. Which is it for the statement "Jesus loves me"?  Is it meant in the same sense as saying that my wife loves me?  My wife is a living person, with whom I have actual social intercourse.  But Jesus of Nazareth died 2000 years ago, so "Jesus loves me" cannot mean the same thing as "My wife loves me”.

So maybe it means something else.  The statement "Jesus loves me" seems more analogous to the statement that "Julius Caesar loves me," but there's no sense in which that statement could be considered true.

I don't want to commit a fallacy here, so I will assume that the statement "Jesus loves me" must mean something else. But what is it? I don't know.

There is also the matter of epistemology. Heddle says he knows that Jesus loves him, because the bible says so. Is this a deductive claim? It sure looks like one, but we seem to missing a premise. (Perhaps it has been omitted, because it's obvious among Christians.)

Or is it an empirical claim? If so, it would be odd to use the bible to justify the claim, since empirical claims are usually verified by actual measurement (that's how we know the claim is meaningful). For example, I could justify my claim that Boston is east of Albany by reading a map of New England, but that's because the map is a simplified model of the terrain, and I can verify the claim easily enough (and I do!) by actually driving east from Albany. But one cannot do this to justify claims about whom Jesus of Nazareth loves, so there's something else going on here. What is it?