In The Odyssey, does Athena help Penelope and Telemachus out of respect for Odysseus or because she deems both worthy?
Athena most assuredly respects Odysseus and helps him throughout The Odyssey, but she also demonstrates that both Odysseus' wife and son are worthy of aid as well.
After many years of Odysseus' absence, Penelope began being courted by all the available Suitors from the neighboring kingdoms. At the point the Suitors began arriving, Odysseus had been gone for seventeen years. Still, Penelope clung to the belief that her husband would return to her, and she devised schemes to put off making a choice of a new husband. First, she plays the trick of the shroud that she is supposedly weaving for Laertes by unravelling all of her work every night. She had said that upon its completion, she would select a new husband. Second, she offers the challenge of Odysseus' bow that whomever can string the bow and shoot an arrow cleanly though twelve axe handles will be her husband. Athena is impressed by Penelope's cleverness as well as her devotion to Odysseus.
When Athena arrives in Ithaca after the meeting in which Zeus decided to free Odysseus from Calypso's island, she comes there disguised as a beggar. It is Telemachus who makes sure that the beggar is fed and well cared for as his guest. Because Telemachus honored the ancient code of hospitality, he is also deemed worthy of Athena's approval and aid.
Consider this quote first:
The goddess...smiled, and stroked him with her hand...and addressed him with winged words..."Bold man, crafty in counsel, insatiate in deceit, not even in thine own land, it seems, wast thou to cease from guile and deceitful tales, which thou lovest from the bottom of thine heart. ...Thou art far the best of all men in counsel and in speech, and I among all the gods am famed for wisdom and craft.”
Athena, the goddess of war, identifies and respect with Odysseus. She is affectionate towards him. While she shows respect to both Penelope and Telemachus for their loyalty, it is her love and respect for Odysseus that drives her actions from beginning to end.