I wonder what the "derivative" volume does to help/hurt the bottom lines of the vendors who actually manufacture the items sold under the Kirkland name.

It usually helps. Costco looks for high margin consumer products that can be sold in high volume. In exchange for reduced margins, the manufacturer gets enormous volume without having to do any marketing or distribution.

Interestingly, Kirkland Signature products are often co-branded. For example, the infamous giant aluminum foil roll says "Reynolds" right below Kirkland Signature. The Kirkland golf balls say Titlist on them. Starbucks originally roasted Kirkland coffee and the packaging plainly said Starbucks on it (I don't think this is still true). After it was introduced, Starbucks noted a measurable increase in store sales around the Costco warehouse, which meant customers were being introduced to Starbucks by Costco. This helped Starbucks go nationwide. Coincidently or not, Costco board member Jeff Brotman was an early, pre-IPO investor in Starbucks.

Similarly, some manufacturers have brands/models that are only sold at Costco. I saw some Shokz Open Run SE headphones at Costco for $80. Regular Open Run headphones (not SE) are normally $130. I emailed Shokz asking them what the difference was. They said the only difference was the color. Presumably, they created a different model so the don't undercut their retailers who are selling the same thing for $50 more dollars.