This is a good question, as it relies on the proper understanding of ἄνωθεν (anōthen) . This word is used 13 times, and in most of the instances it is an adverb defined as "from above" meaning God or heaven (see here).
But it is clear in this case the "greater sin" cannot be attributed to heaven, although the "authority" over Jesus was given by His Father-in Heaven. Pilate was responding to a request from the Chief priests and Sanhedrin to put an innocent man to death-a man who's innocence he learned of from his wife(Mt. 27:19). The manner of death which they were requesting was crucifixion, which only Pilate had the authority to do.
But the Chief priests and the Sanhedrin had the authority "under the law" to put to death anyone for blasphemy, which conclusion they came to in Matt. 26:64-65,
"Jesus saith unto him, Thou hast said: nevertheless I say unto you,
Hereafter shall ye see the Son of man sitting on the right hand of
power, and coming in the clouds of heaven.
65Then the high priest rent his clothes, saying, He hath spoken
blasphemy; what further need have we of witnesses? behold, now ye have
heard his blasphemy. 66What think ye? They answered and said, He is
guilty of death.
The "greater sin" was that although they "sat in Moses's seat", and therefore did have authority over Jesus under the Law,(Matt. 23:1-3),
Then spake Jesus to the multitude, and to his disciples, 2Saying, The
scribes and the Pharisees sit in Moses' seat: 3All therefore
whatsoever they bid you observe, that observe and do; but do not ye
after their works: for they say, and do not.
Therefore, the Father(from above ἄνωθεν (anōthen), had given authority to the Chief priests and scribes, and furthermore, they "knew" whom they were crucifying, John 9:40,
And some of the Pharisees which were with him heard these words, and
said unto him, Are we blind also? 41Jesus said unto them, If ye were
blind, ye should have no sin: but now ye say, We see; therefore your
In His parable about the Wicked Servants(Mk. 12:1-12), Jesus alluded to the scribes and Pharisees;
6Having yet therefore one son, his wellbeloved, he sent him also last
unto them, saying, They will reverence my son. 7But those husbandmen
said among themselves, This is the heir; come, let us kill him, and
the inheritance shall be ours. 8And they took him, and killed him, and
cast him out of the vineyard. 9What shall therefore the lord of the
vineyard do? he will come and destroy the husbandmen, and will give
the vineyard unto others.
Furthermore, they knew He was talking about them,(vs 12)
And they sought to lay hold on him, but feared the people: for they
knew that he had spoken the parable against them: and they left him,
and went their way.
Conclusion: They had been given the authority "ἄνωθεν" to put Jesus to death; yet they knew who He was and what they were doing. Therefore, they incurred the "greater sin" than Pilate, who was attempting to appease a restless population, and against the counsel of his wife, decided to have Jesus crucified; although he made a 'public gesture' of absolving himself.
In Jesus's Final Words,"
"34Then said Jesus, Father, forgive them; for they know not what they do,"
He fulfills His Purpose; as the once and for all sacrifice, extending forgiveness not only to those who put Him to death, but to all men in every generation who have sinned;
27Now is my soul troubled; and what shall I say? Father, save me from
this hour: but for this cause came I unto this hour. 28Father, glorify
thy name. Then came there a voice from heaven, saying, I have both
glorified it, and will glorify it again..
Therefore, it was to the glory of the Father that Jesus submitted Himself to the authority of those who put Him to death.