[et-al]

I'm not familiar with this slang: what's a big plate?

[allan_s]

It's a slang for somebody fat. 子 does not carry a specific meaning it is more a character with grammatical function to nominative

[dirteater_]

the commenter's username (i'm guessing they mean 大胖子, feel free to google translate)

[dapangzi]

This is the correct.

I was first called this by a Chinese classmate from Beijing with a biting sense of humor, when I was at university in Tokyo.

We got on really well, to be clear. :)

Hanging out with him was actually how I got started with Mandarin, probably why I chose this username.

[dapangzi]

胖 (pàng) means fat, vs 盘 (pán), which means plate.

Quite alright! We have to make mistakes to learn!