She [Marianne] was perfectly disposed to make every allowance for the colonel [Brandon]'s advanced state of life which humanity required.
In particular what is meant by advanced state? And what exactly is required by humanity?
First, recognize that Austen's verbiage can seem excessively polite when compared with modern English. "She was perfectly disposed" means "she would", and "his advanced state of life" is a euphemism for "he is old".
Today, if we wanted to be similarly polite, we would instead say, "he is elderly," or, "at his advanced age," or sometimes, "at his time of life". Not really all that different, but then again these are not normally used in casual conversation.
Second, the adverbial phrases are in a confusing order. We could rewrite as:
She was perfectly disposed to make every allowance which humanity required for the colonel's advanced state of life.
In other words, she was more than happy to do as much as she could to accommodate the elderly colonel. I've not read the novel, but I assume he had some (or perhaps many) infirmities as a result of his age.
[Edit] Apparently in the novel Colonel Brandon is only 35, which apparently Marianne considers elderly and decrepit. In this case the phrase is very likely meant to be satire.