He was born before Khandav-Dahan, there is a citation which introduces every son of Draupadi along with a nice description of Abhimanyu.
Here is when Abhimanyu was born ( This citation is before Khandav-Dahan and before Arjuna got his Gandeev)
..." Then Subhadra, the favourite sister of Kesava, gave birth to an illustrious son, like Puloma's daughter, (the queen of heaven) bringing forth Jayanta. And the son that Subhadra brought forth was of long arms, broad chest, and eyes as large as those of a bull. That hero and oppressor of foes came to be called Abhimanyu. And the son of Arjuna, that grinder of foes and bull among men, was called Abhimanyu because he was fearless and wrathful. And that great warrior was begotten upon the daughter of the Satwata race by Dhananjaya, like fire produced in a sacrifice from within the sami wood by the process of rubbing. Upon the birth of this child, Yudhishthira, the powerful son of Kunti, gave away unto Brahmanas ten thousand cows and coins of gold. The child from his earliest years became the favourite of Vasudeva and of his father and uncles, like the moon of all the people of the world. Upon his birth, Krishna performed the usual rites of infancy. The child began to grow up like the Moon of the bright fortnight. That grinder of foes soon became conversant with the Vedas and acquired from his father the science of weapon both celestial and human, consisting of four branches and ten divisions."...
Now Abhimanyu has been born before Khandav Dahan, the next Parva describes the Khandav-Dahan.
Now, below Dhritsashtra says that Arjuna carried Gandeeva for 3 and 30 years
..." Three and thirty years have passed away since the time, when Arjuna, having invited Agni, gratified him at Khandava, vanquishing all the celestials. We have never heard of his defeat anywhere, O child. Like the case of Indra, victory is always Arjuna's, who hath for his charioteer in battle Hrishikesa, endued with the same character and position. We hear that the two Krishnas on the same car and the stringed Gandiva,--these three forces,--have been united together. As regards ourselves, we have not a bow of that kind, or a warrior like Arjuna, or a
charioteer like Krishna "...
Arjuna got Gandeev during/after Khandav-Dahan and Abhimanyu was born before it. Dhritashtra says that Arjuna has been carrying Gandeev for 33 years. So, Abhimanyu was atleast 33 years old when he died, not 16. Yes, he was comparitvely smaller to his opponents but in no way he was 16.
Correct me If I am wrong.