Looking for a contex-free grammar for the following language
Hint: you want to measure size of $x$ and $y$, and still have the sum of the two in the end. so when you read them, you will need twice their size: one for $x'$, and one for $z$.
Start with designing a PDA, it seems easier than a grammar.
Then you can use a PDA-to-grammar translation to get the wanted grammar.