Inferentiability is a step too far! There is the word inferable, meaning "being able to be inferred". And it is quite usual to extend -able adjectives to be -ability nouns.
So I suggest you should use inferability. While it's not in the dictionary, it is an intuitive extension of inferable, so noöne will have trouble understanding you.
This would improve the inferability of someone's height, given their weight.
To give a little weight to my answer, here are some examples of inferability in the wild:
To regard sentence-tokens as the entities which enter into inferability relationships would be to regard questions about inferability as arising anew for each utterance of a given set of sentence tokens.
— Gary Iseminger (1968), Introduction to Deductive Logic, New York: Appleton Century-Corfts Education Division.
At first there is natural temptation to suppose that such a gradation must vary with the varying inferability of the hypothesis from the experimental data.
— Theo A. F. Kuipers (Ed.) (1987), What is Closer-to-the-truth?: A Parade of Approaches to Truthlikeness, Amsterdam: Rodopi.
In (82) above, this inferring is done by virtue of the referent belonging to the same scenario as some other, previously mentioned, referent, but, as we will see later on, inferability can be of a different nature.
— Ronald Geluykens (1994), The Pragmatics of Discourse Anaphora in English: Evidence from Conversational Repair, Berlin: Mouton De Gruyter.