Bigger than I (am big)," is correct. You'd never say, "Bigger than me (is big)."
The correct sentence is "He is bigger than I". Would you say" he's bigger than me am."? No, but you would say, "he's bigger than I am." Drop the "am" and what do you get?
English can be a very confusing languages as far as its grammatical rules are concerned. The proper way to write the above sentence is as follows:
He is bigger than me.
The key is that I is never used while doing comparisons with another individual.
He is bigger than me.
The key is that I is never used while doing comparisons with another individual.
I don't think any of the above explanations are all that insightful, and it's still unclear what is correct. Consider the following two examples, which I think are correct:
She weighs more than I (weigh).
She is as big as I (am big).
But it doesn't seem right to say: She is bigger than I (am bigger), because there is another implied comparison: I am bigger than what/whom? Also, I don't think the implied is "She is bigger than I am big." Correct would be something as follows:
She is bigger than him than I am bigger than him. So she is bigger than me. She is biggest. I am big. He is not so big.
She weighs more than I (weigh).
She is as big as I (am big).
But it doesn't seem right to say: She is bigger than I (am bigger), because there is another implied comparison: I am bigger than what/whom? Also, I don't think the implied is "She is bigger than I am big." Correct would be something as follows:
She is bigger than him than I am bigger than him. So she is bigger than me. She is biggest. I am big. He is not so big.