If you write a library, or expose a public interface, I do expect a lot of unit tests. Unit tests can run offline, fast, during build time. I don’t mind integ-unit tests that perhaps simulate a database in memory to avoid mocking the entire storage layer. I rather have tests that are technically integration tests as they include more than, well, a unit, as long as they are idempotent, test mainly one thing, and can run fast and offline. Not sure if there is a term for it but I call these integunit tests... (probably the worst name possible)
But unit / unit++ tests are not just for you, they are for me, they give me confidence I can touch your code without inadvertently breaking something critical that you may have missed in your acceptance tests. It gives you peace of mind to be able to refactor. An acceptance test may tell you they something broke, but a good unit test will show you exactly where.