I have a distributed application with a dozen docker containers that run across a few machines (< 5). I want to package this app so customers can easily deploy on their machines or in a cloud service. Currently, I'm using kubernetes because it abstracts away all the hardware issues, but it feels like overkill.
Is there a lightweight alternative to kubernetes?
Kubernetes is not actually overkill but an excellent solution for your problem. The only issue is that your customers might be new to Kubernetes, this can make deployments on their side more difficult.
To make things simpler, you can start with Dockerswarm, and then work on good documentation towards a Kubernetes adoption. FYI, Docker Inc now recommends Kubernetes as the ultimate solution to container orchestration on a cluster of compute nodes.