For one thing you need more platys, they like to be in ggroups of at least three. If he's paper thin he's probably starving, try to get him some food and seeif he eats it. How log have you had him? When did his mate die?
I agree. Maybe he will gradually improve and become more comfortable if there are more platies in your tank. Companionship gives shoaling fish a sense of security. if he is starving from lack of food or has lost the will to eat the feeling that he is in danger and alone wont help. Keep up the water changes, feedings (don't overfeed!) and consider adding some company. Perhaps your fish is also just old and the time is coming for him to die. that cant be helped only postponed.
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