St. John repeated this word 'beloved' each time he calls him.
Watch this wonderful expression
"To the beloved Gaius, whom I love in truth"
It's not a friendship' love or just love but it's love in Christ; it's love in truth.
This love is not about covering the friend's mistakes, but it's about loving each other in Christ.
If your friend has some weaknesses, you should treat it kindly, quietly, patiently, with longsuffering and covering it for you love him in truth.
This is the first person.