If anybody has firm metrics on this, they are keeping them to themselves.
There are definite advantages in introducing an application tier. It allows you to set up entity beans representing validation data (see your other query) which greatly reduces the load on the database and thus response times.
The disadvantage of a separate application server tier is that you introduce network I/O on all calls between the two tiers.
The disadvantage of deploying the application server with the web tier level is that each web server will keep its own copy of entity beans, and will incur some I/O and database effort to keep it up to date.
Which disadvantage is larger will depend on the exact circumstances.
One possible solution is to deploy in two tiers, and then to put a cache in the web tier that minimises calls to the application tier.
I can let you have code for validation data, and the associated cache, if this would be helpful to you.