Help in interpreting this graph? Assets/Liability ratio
Wouldn't it be better to use equity instead of assets for a measure of
  leverage?


No, but the correct ratio is

$$\frac{\text{Assets} }{ \text{Equity}}$$

Reasoning: with "leverage" we want to obtain information on how much a company uses debt for financing. And we want to have the correspondence "higher leverage $\to$ more debt financing".

Moreover, in order to be consistent with the definition of "leverage" ("the exertion of force by means of a lever"), we want the information on debt to be in the denominator, since we want to form a ratio.

In order to achieve all these together, we need to put equity on the denominator, so that lower equity (implying higher debt for same level of assets) increases the value of the ratio, and we get the higher leverage.