Sirius is always at the forefront of his mind; he always makes space for Sirius amongst the jungle of memories and stray thoughts and the worries that Voldemort may finally kill him. At least before he attempts it himself.
Sirius is always there in his mind, he is constantly thinking of the ways he could have utilised his naive mind and saved him, but at this point, all he has achieved is a bleeding heart and enough regrets to weigh him down like a dozen and more boulders.
Too heavy to keep it on his mind when running from Voldemort and his death eaters. Too heavy unload his burdens and growing sorrows on his friends.
So, he did the only thing he could do, even though it really wasn’t, the only thing it was, was selfish.
He walked up to the veil and jumped.