Kurtosis does not just measure tail heaviness. It also measures peakedness. A distribution that is similar in the tails but more peaked will tend to have higher kurtosis than one that is less peaked.

Another way to think of kurtosis is as follows:

Define the 'shoulders' of a density as being at $\mu \pm \sigma$. Then the kurtosis can be thought of as (a constant plus) the square of the variabliity about the shoulders. That is, the more the probability moves away from the shoulders, the bigger the kurtosis becomes.

See the first paragraph here:

http://en.wikipedia.org/wiki/Kurtosis

Kurtosis does not just measure tail heaviness. It also measures peakedness. A distribution that is similar in the tails but more peaked will tend to have higher kurtosis than one that is less peaked.

Another way to think of kurtosis is as follows:

Define the 'shoulders' of a density as being at $\mu \pm \sigma$. Then the kurtosis can be thought of as (a constant plus) the square of the variabliity about the shoulders. That is, the more the probability moves away from the shoulders, the bigger the kurtosis tends to become.

This broad tendency is not a theorem by any means; it's possible to arrange to move the probability around in such a way that the peak increases while the kurtosis goes down. [The issue comes down to how you define "similar in the tails".]

See the first paragraph here:

http://en.wikipedia.org/wiki/Kurtosis