Heh, I usually show this movie during my presentations.
First of all, this has nothing to do with surface tension. Those are just vortex rings that are only visualised by dolphins by filling their cores with air (you can see this happening about 0:12).
At first the rings grow to optimize vortex core size, but the most increase is made by the fact that dolphins make water flow through the ring (you can see they kinda push the rings through the water). The speed of each point on a vortex ring in localised induction approximation is $\dot{\vec{s}}=\frac{\beta}{R}\hat{\mathbf{b}}$, where $\hat{\mathbf{b}}$ is a binormal vector of the ring, $\beta$ is constant and $R$ is the diameter of the ring; so when the dolphin pushes the ring its effective speed decreases and so its diameter must increase. Not counting friction, free ring holds its diameter.
The making of small rings is due to the fact that dolphins distort the ring making it reconnect with itself. Two rings are created in the process, small and big, yet the big degenerates in eddies created by the dolphin swimming past it to play with the smaller one.
