Preheat oven to 350 degrees.
Rinse tilapia loins and pat dry. Season each loin with salt and pepper.
Tear four large squares (14" x 12") of parchment paper and fold in half. Draw a half-heart on half of the paper, using as much of the paper as possible. Cut out the half-heart shape with a pair of scissors or kitchen shears (when you unfold it, you'll have a whole heart!).
Place one tilapia loin on one half of each parchment paper heart, placing the fish about 1/2" away from the fold. Arrange tomatoes, onion, garlic, capers, and olives evenly on top of each loin, dividing the ingredients equally among the four packets. Drizzle each loin with 1/2 tbsp. of olive oil and 1/2 tbsp. of red wine vinegar.
To make each packet, fold the empty half of the parchment paper heart over the ingredients and line up the edges of the 2 halves. Start at the broadest part of the packet: working in ~2" sections, start folding the edges of the paper upward toward the top of the packet, leaving about 1/2" of space all around the fish. Move on and fold the next section toward the top of the packet; repeat until you reach the narrow part of the parchment paper. Twist the remaining paper and fold under the packet (you can also secure it with a staple or paperclip). Set the packet on a baking sheet and repeat with the other packets.
Bake for 25 minutes, or until the fish is flaky and no longer translucent (be very careful opening the packets to avoid steam burns). Serve and enjoy!