Here's why:
* "Two-bits" was a slang term for a small amount of money, typically 25 cents.
* "Worth" implies that the opinion or comment is worth something, even if it's just a little bit.
Example:
"Everyone was excited about the new project, but John had to get his two-bits worth in and point out all the potential problems."
The idiom suggests that John might be interrupting or being negative, but he feels the need to share his opinion regardless of the context.