LayerSizeFunction

is an option for TreePlot that gives a function to specify the relative height to allow for each layer.

Details

LayerSizeFunction->f specifies that the difference of coordinates between layer n and layer should be proportional to .
The root or top vertices are taken to be at layer 1.
With the default setting DataRange->Automatic, LayerSizeFunction is taken to give the actual coordinate difference between layers.

Draw a tree with the first level of height 1, and the second of height 2:

Plot a binary tree with random layer size:

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