Goblin - Both male leads have aspects of this. They are powerful supernatural beings, and there are many scenes that involve them showing off their powers - but they're also goofy and awkward, and they are especially soft, cute, and vulnerable when it comes to their love interests.
I'm Not a Robot - the ML has developed an extreme, life-threatening allergy to other people that is triggered by touch, so he essentially lives an isolated existence in his home and gradually falls in love with an "android" (who is a woman being paid to pretend to be the android he purchased). Both leads are super cute and sweet.
Introverted Boss - the ML struggles with extreme social anxiety while the FL is outgoing and bubbly. He is often misunderstood as being cold, but he's actually pretty sweet - he just has to overcome his shyness.
Secret of the Three Kingdoms - the ML is unusually compassionate, gentle, and naive. His best friend/older brother-figure spends most of the drama protecting him while his new wife - the empress - teaches him the ropes of being the emperor. She is generally the stronger and more mature partner in the relationship, although eventually the power dynamic shifts as the ML becomes more confident and chooses to do whatever he thinks is best. He maintains his innocent, optimistic outlook, though.
Strong Woman Do Bong Soon - the FL has superhuman strength and she has been hired to protect the ML. He isn't threatened by her strength; he is drawn to her because of it. I wouldn't say he's "weak," necessarily, but I think cute and needy could apply. He's pretty forward with his feelings for the FL and his desire to pursue a relationship with her, and he has a playful, light-hearted vibe.
What's Wrong With Secretary Kim - If you want needy, this ML is your man. He doesn't want to lose the secretary that he has relied on for years, and when he finds out that she's quitting to figure out what she wants in life and find a spouse, he proposes to her on the spot. He can be a bit overwhelmingly arrogant at times - it's sometimes obnoxious, sometimes funny/cute. This honestly isn't my favorite drama but it does have a lot of cute/fun moments (and a lot of people love it a lot more than I did, it seems).