Final answer:
The Gardiners realize the mutual affection between Elizabeth and Darcy through their interactions at Pemberley, indicating the progression of their relationship.
Step-by-step explanation:
The Gardiners, upon watching Elizabeth and Darcy interact at Pemberley, realize the depth of the affection between them. Their observations lead to the awareness that Darcy is deeply in love with Elizabeth, indicated by his demeanor and attentiveness towards her. Similarly, Elizabeth's ease and happiness in Darcy's presence suggest a shift in her feelings, from previous skepticism to a burgeoning respect and affection for him. The Gardiners' realization marks a pivotal acknowledgement of the evolving relationship between the two central characters in Jane Austen's novel, Pride and Prejudice.