If flow is q, and pressure is p, The linear flow characteristic "R" is defined such that p = (q)(R)
This is directly analogous to V = IR in ohms's law, in the electrical analogy.
If we differentiate p=qR, we get dp = (dq)(R)
In this case, pressure is being reckoned in units of height, for which it should be mentioned that p = (ρ)(g)(h) where the greek letter rho (ρ) is the liquid density, g is the gravity (9.8m/s^2), and h is height.
Thus we write dh = (dq)(R)
We substitute this into equation 2.68:
(A)(dh/dt) = qi - q1
(A)(R)(dq/dt) = qi - q1
which is a first order ODE, so the solution is exponential form, and the time constant is AR, which is of course proportional to R.
On an qualitative/intuitive level, bigger R means more constricted flow, which means less flow for any given pressure aka height, which means it takes longer for the tank to drain, which means larger time constant. Similarly, bigger A means there is more liquid to be drained for a given height, which means it takes longer, which means larger time constant.