There is no additional charge for using AWS App Mesh. You pay only for the AWS resources (EC2 instances or requested Fargate CPU and memory) consumed by the lightweight proxy that is deployed alongside your containers.
Related product pricing
Amazon ECS with Fargate
You pay for the amount of vCPU and memory resources that your containerized application requests. vCPU and memory resources are calculated from the time your container images are pulled until the Amazon ECS Task* terminates, rounded up to the nearest second. A minimum charge of 1 minute applies.
See the AWS Fargate pricing page »
Amazon ECS with EC2
You pay for AWS resources (e.g. EC2 instances or EBS volumes) you create to store and run your application. You only pay for what you use, as you use it; there are no minimum fees and no upfront commitments.
See the Amazon ECS pricing page »