BELATED

Writing an email the other day; "Happy belated St Paddy's Day", I thought to myself; "What the heck does belated mean?" I didn't use the word 'heck' but the meaning was the same. A little lightbulb came on in my head. Not like a cartoon light bulb with a big flash. No, more like a single christmas tree light, or even one of those low power TV remote control LED lights. And I said to myself, "I wonder, yes, I just wonder, does 'belated' come from 'be late'?"
It briefly made me feel good to have a thought like this. But then it made me feel bad because I thought of two more things.
1. If it comes from 'be late', then why haven't I figured it out before now. And,
2. Surely it can't be that simple. It doesn't seem logical to make new words by joining two old words. Surely that's not right because the past tense should be 'beenlate', and not 'belated'; 'Happy beenlate St Paddy's Day'??? I don't know. So I looked in a dictionary, but that made my eyes hurt and I think the fuse blew and my light bulb popped.