Jacob Marshall was taken to hospital from an address in Belsford Way, Speke, Liverpool, on Friday as the ambulance service alerted police with their concerns.
A 23-year-old man from Winsford, Cheshire, was arrested on suspicion of murder and has been conditionally bailed pending further inquiries by Merseyside Police.
In a tribute issued through police, Jacob's family said: ‘Our little puddin', our gorgeous boy... baby Jacob. We will miss his beautiful soul and his cheeky smile.
‘He always had us in fits of laughter with his cute mischievous ways. He had the most amazing little personality, learning new things each and every day.
‘He'd tell us 'oooh what's that?', pointing in a different direction just so he could rob your biscuit. He had the most amazing ways.
‘He just loved everyone around him. Jacob's mum and his big brother will miss him massively, as their lives have now changed forever. Mum and all the family are completely heartbroken.
‘All of our worlds have been crushed and our lives will never be the same again.
‘We will talk of Jacob every day and of all the amazing memories we all got to make with him.
‘He will live on in us all forever, our gorgeous baby Jacob.’