Carson Price, from Hengoed, was found in Ystrad Mynach Park on Friday 12 April.
He was taken to the University Hospital of Wales in Cardiff where he later died.
In a statement, the family said they wanted to urge people to talk about the "devastating consequences that drugs can have".
On Friday 12th April, our lives changed forever when our little boy was taken away from us.
They also thanked Carson's friends and the local community for organising the vigil saying it has given them "great comfort".