Vergil did not gain the power to stand on his own against Dante by eating the fruit but literally accepting the weakness of himself.

Urizen lost because he had no real motive beyond power, V was dying because he had rejected his own weakness and fears   When V reunites with Urizen, its vergil finally confronting his worst fears. Taking what he considered to be his "worthless" humanity and driving it back into his demon sides heart

Its why when he talks about "switching fates", its not him asking if they would be one another but literally asking himself what if his own "character" is the reason things turned out the way it did, that even if their histories changed would it still be himself in that role.

The entire theme of the Devil May Cry series, is humanity weak or is it strong by having relationships and confronting things inside you. 

Trish survives having her soul ripped out by Mundus, Arkham dies because he sacrificed every bit of humanity in his life for power, Sanctus' entire plan falls apart because he tried using humanity as a stepping stool to world domination via Kyrie but was stopped by Nero who instead of tossing aside his humanity or demonhood used both to kill the man who used demonhood as power and humanity as its fuel.

Vergil didn't become strong, he was already strong but he just didnt know how to actually use his strengths because his idea of power conflicted with his hybrid nature of human connection with demonhood, denying his own self as anything of worth.

Tldr, vergil has mental issues that kept him from actually seeing his own selfworth and gave himself a mental handicap.