what does " pining her heart away"here mean?
her lameness became more confirmed as tiem went on, and she seldom or never left the house in the long southern thoroughfare, where she seemed to be pining her heart away. ‘Why mayn’t I say to Sam that I’ll marry him? Why mayn’t I?’ she would murmur plaintively to herself when nobody was near.

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the function that the "do" serves in this sentence is to place emphasis, that's why it's called the emphatic do

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"pining" = to miss somebody to yearn/long for them to come back.
"pining" refers to a mental state.
"pinIng her heart way" is a term we use to describe someone who is in emotional turmoil over the loss of a lover, partner, friend, family member, pet etc.
The loss can be because of death or a break up.
It describes the initial period and behaviour of people suffering such loss. Commonly they lock themselves away from others and do not leave the house for a while.