You asked what an American would call this, and although I'm a native British English speaker, I'm fairly certain there isn't a US term for this. The concept of a couple where one is fat and the other is thin is a really common trope on US television, from The Honeymooners to King of Queens, The Simpsons and Family Guy... if they had a phrase for it, we'd have heard it.
Two people who are seemingly mismatched are sometimes referred to as an "odd couple". This doesn't only refer to size or weight, but if you said it about a couple who were markedly different in size I think it would be clear what you meant. Another similar idiom is "strange bedfellows". Again, this could refer to anything characteristic that makes two people seemingly an odd match.
There is a British expression to describe something that looks too small because it is next to something big - "it's like a pea on a drum". I've not heard it used about people before, but if someone said "they are like a pea and a drum" I'd get that it was a variation of that idiom.
I can't think of any specific idioms about the difference in two people's size or weight. Creative writers would probably think up their own. "An elephant and a chicken" is certainly understandable to me, but it definitely doesn't sound English in origin. It sounds like what it is - a translation of an idiom from another language.
To be clear, comments about people's weight or size are generally considered very rude. I'm not endorsing "fat shaming".