Well,theres where you wrong.Lol i'm getting this from the dubbed series.A quote came to my head when you said "Before he was controlled by Babidi"
Goku: I'm amazed Vegeta,these last 7 days at Other World I've been through the most intence training sections,but we're still completley even.I guess this whole time you've been pushing yourself harder then I have.
Vegeta:That may be true,I've pushed my self to the edge of my limits and beyond,but you've been born with a natural talent far beyond my own,no amount of training could close the gap between us.I realised that now,it was made painfully clear to me as I watched your fight with Babidis' monster.
---Da di da Goku Fights Yakon---
Vegeta: Imagine my shock,to see the undeiable truth,to see that how hard I tried,I would never be able to catch you,A warrior prince forever living in the shadow of a low level clown.
Vegeta: So thats when I secretly made up my mind
Goku: You mean you??...you FOOL!! You delebrity let yourself fall under Babid's spell.
Vegeta: Yes...,I saw the power of Babidi's magic at the......... *ETC Videl gets owned*
Vegeta: The peopel who had seen those fighters in the previous tournament didn't understand how they'd become so powerfull.But you and I know DONT WE.It was Babidi's magic,and I knew that what he's magic had done to those fighters it could also do to me!! I knew that if I knew that If i allowed myself to fall under his controll the difference in our powers would DISAPEAR!
I'm quite pleased with the results,even if they do come at a price.
There we go...it shows that Vegeta needed Babid's magic to go SSJ2
-GuZzie