Main Character falls in love with Love Interest whose out of their league?

https://kisskh.at/article/2017/01/20/5-classic-romance-jdramas-that-you-need-to-watch

• Hana yori dango – it’s a must see it’s the classical Cinderella story but one of the bests ever done (2 seasons and 1 movie)
• Buzzer Beat – good romance drama about 2 people that meet and fall in love but first they have to find the perfect timing for them to be together 
• Love Shuffle – it’s a story involving 4 couples and how they learn what love is
• Pride – a classic romance drama with a mature couple who grow and learn from each other and also heal each others wounds
• Tatta Hitotsu no koi – a very good romance and it’s a Cinderella story but inverse (rich girl, poor boy)
• Hotaru no Hikari – this has 2 seasons and a movie, and it’s a bout a couple that has to live together due to some circumstances and gradually fall in love
• We married as a job - As mentioned before this one is compared to Because this is my first life. I liked both of them but I'll have to say I liked better how they managed the "contract relationship" at the final episodes here. 
• Soratobu Kouhoushitsu - I like this one, because is also about 2 persons who had their dreams broken about their ideal jobs but with the help of each other discover a new passion in life. 
• Kahogo no Kahoko - This one is pretty sweet and lighthearted, the OTP is very cute and it centers alot on family.
• Boku unmei no hito desu - This one is also pretty lighthearted, the male lead is very sweet and kind and it's totally focused on romance

AS for your main topic "Out of their league"

• Takane no Hana
• Densha otoko
• Black prince and wolf girl

• Closest Love to heaven

Most of the ones I know are Korean 

Itazura na kiss

Busu no Hitomi ni Koishiteru