I buy oranges by weight or by the weight

[ROBINDESBOIS]

which one is correct? Similar expressions?

[Rusty]

These expressions may be interchangeable in some instances.
When you use the article, you kind of imply that there's a specific weight you're looking for.

[Tomisimo]

Without the article sounds a little more normal for me.

Another option, at least in AmE, would be "by the pound".