> Does costco get some extra benefit if the consumer buys Kirkland from costco ?

Yes. Costco positions their store brand as a major part of their appeal. This attracts more consumers to their stores, which

A. Increases membership, for which there's an annual fee, and

B. Increases traffic, increasing sales of high margin items as well as the low margin store brand.

If Costco sells their products at other stores they are effectively shooting themselves in the foot: It is providing the lower price of their products to be accesed without paying for a membership; which is how Costco makes money.

Costco's value proposition is that they make (on average) no net income from sales of their products, and that you will find no other competitor who can sell the same quality products at a cheaper price (because costco's already selling them as cheap as possible). In exchange, they ask you to pay a membership fee, which is their net income.

If they were to give away their reputation to other sellers by letting them sell their QC'd products, they would be lowering the value of their memberships.