And, behold, they brought to him a man sick of the palsy, lying on a
bed: and Jesus seeing their faith said unto the sick of the palsy;
Son, be of good cheer; thy sins be forgiven thee. (Matthew 9:2, KJV)
When Jesus saw their faith, he said unto the sick of the palsy, Son,
thy sins be forgiven thee. (Mark 2:5, KJV)
Jesus used terms of familiarity and endearment to address people because of his great love toward them which he was unable to conceal. More than this, as the poor sufferers heard such affectionate terms used to address them, it gave them hope and comfort in knowing that they were accepted of him, their Savior.
Two particular cases of this are on record: the palsied man of this question, and the woman who had the issue of blood for so many years--recorded in three of the gospels.
But Jesus turned him about, and when he saw her, he said, Daughter, be
of good comfort; thy faith hath made thee whole. And the woman was
made whole from that hour. (Matthew 9:22, KJV)
And he said unto her, Daughter, thy faith hath made thee whole; go in
peace, and be whole of thy plague. (Mark 5:34, KJV)
And he said unto her, Daughter, be of good comfort: thy faith hath
made thee whole; go in peace. (Luke 8:48, KJV)
But Jesus also pitied those women who mourned his fate as he passed them on the way to Calvary.
But Jesus turning unto them said, Daughters of Jerusalem, weep not for
me, but weep for yourselves, and for your children. (Luke 23:28, KJV)
Jesus began his ministry at the age of 30, and ministered only three and a half years, being crucified at the age of 33. It is quite probable that when he said "Son" and "Daughter" to these two afflicted ones, they were actually older than he was.
We know the woman had had her issue of blood for 12 years. Assuming that she had begun to have the issue while only a teenager, she would still have been nearly the same age as Jesus--certainly not young enough to be his daughter. We also know that the palsied man had been in his paralyzed condition for many years, though we are not told exactly how many. Again, he cannot have been much younger than Jesus, if he was at all.
Jesus did not use these terms merely to make himself appear to have a superior status--he used them with tender affection, demonstrating his love and acceptance of them. And, of course, Jesus was speaking on behalf of the Father, his Father and their heavenly Father, who loved, accepted, and healed them.