Truth is Link always had a soft spot for him. That's why when he saw that Fledge was so earnestly training to get stronger he didn't even hesitate to help him. This was his friend. His friend who always cowered behind him when there were bullies or needed his help when he had chores. And now his mostly helpless friend was trying to better himself. To say that Link was proud would be an understatement.
Link went there every night he could just to encourage Fledge. He still did all he could to save Zelda but whenever he had a bit of spare time he would fly back to Skyloft in hopes of seeing his special friend. Soon he even started coming during the day just so they could hang out for a bit. Link had been so busy with knight training that he hadn't had a chance to spend time with Fledge like this in a long time. Ironic that he finally found the time when he was busier than ever.
But no matter how busy Link was, he needed to go back to Skyloft every now and then. Sometimes he would just lose all faith in himself and think to himself that he would never find Zelda. In those moments, when he had lost all hope, he would return to Skyloft and Fledge would give him all his confidence back. Because no one was as kind as Fledge. He always knew just what to say to make all of Link's troubles disappear. More than that, Fledge actually believed in Link. Other people would give Link words of encouragement but their eyes never sparkled with true belief like Fledge's did. Fledge looked at Link as if he could do anything. And when Fledge looked at him like that, Link felt like he could do anything.
So Link needed Fledge and Fledge needed Link. In hindsight it seems almost too obvious that it was going to happen. That one night, after Fledge tired himself out from his training, he would roll on his back, and while Fledge was just laying there, that Link would lean over and gently bring their lips together.
