The branching ratio for a certain channel $i$ is given by the ratio of its partial decay with $\Gamma_i$ and the sum of all partial decay widths:
$$
BR(H \rightarrow i) = \dfrac{\Gamma_i}{\sum_j \Gamma_j}
$$
where the $\Gamma_i$ depend on the Higgs mass. If a new channel opens up or becomes important (such as the decay to a pair of W bosons at around twice the W boson mass), other channels become less likely, the new channel 'steals' branching ratio from the others.
(An analogy in daily life is the following: finding a cure for heart diseases reducing the probability of dying from a heart attack would increase the risk of dying from other diseases. At the same time, the overall life expectancy would go up. In particle physics, the total width $\Gamma = \sum_j \Gamma_j$ of a resonance is inversely proportional to its mean lifetime, longer living particles have smaller total width).
To illustrate this, here is a plot of the partial and total decay width (values taken from http://arxiv.org/abs/1307.1347 , Tables A.1-14):
You'll notice that the widths for decays to WW (solid blue line) and ZZ (solid red line) increase more rapidly at twice the W and Z mass respectively (note that the y axis is logarithmic) at which point both bosons can be produced on-shell.
