Dave had noticed.
What? You think he didn't? Of course he did! One of you best bros (let alone crush...) starts acting differently, of course you notice!
Karkat had to have lost at least twenty five pounds in the past month. Dave honestly wasn't sure what he should do....
While yes, he noticed karkat acting strange and losing way too much weight, that doesn't mean he knew how to help him...
So he consulted his sister.

"Karkat's acting weird"
Rose was silent for a moment
"Did you consider talking with him?" She asked slowly.
Dave paused "uhm... Well... I did consider..."
Rose sighed softly and chuckled "I suggest you go talk with him David. I've noticed as well but it's not in my place to talk with him, now is it? You are much closer friends with him then I am"
Dave sighed as well and nodded "I guess you're right... I... I guess I'm just nervous to talk to him about it..."
Rose smiled gently "That is understandable, Dave."
The blonde haired boy looked to the side as he adjusted his shades "what if he doesn't know what's wrong himself?"
Rose shook her head "one thing at a time. Go talk to him first" Dave sighed again as he was shooed out of Rose's room.

And so, Dave walked to the troll boy's room and knocked on the door

"Karkat...?" Dave nervously looked around "look man, I know you're in there... If you don't let me in then I'll come in myself!" Dave warned. Still, all he got was silence.
The blonde tried the door and was exceedingly surprised to find that it was unlocked.
Dave took a deep breath before he slipped into the room. It was really dark inside and Dave was tempted to turn on a light but instead he just slid off his glasses and put them into his pocket. Dave shut the door behind him and started feeling around the nearly pitch black room. Eventually he made out a small figure sitting in the corner.
"Karkat...?" He asked gently. The figure lifted its head from it's arms "Dave..." He mumbled.
Dave smiled sadly and sat down next to Karkat.
The little troll boy looked at him for a moment "you aren't wearing your glasses..." He mumbled just as quietly as before.
Dave inwardly cursed trolls' amazing night vision.
Dave sighed and shook his head "I'm not... It's too dark in here for me to see with them on"
Karkat was silent for a little bit "you have pretty eyes..." He whispered.
Dave blushed lightly "thank you"
He leaned against the wall "what's been going on Karkat? Why have you been acting so strangely?"

Way to get to the point Dave.

Karkat bit his lip and shook his head "I haven't been acting different..." He lied.
Dave rolled his eyes "it's pretty obvious, Kitkat. Something's up."
Karkat blushed at the nickname and looked away "why do you care...?" He mumbled.
Dave frowned "Karkat... You're my friend. I care because I'm... I'm pale for you...?" Dave asked, unsure if the terms he was using was right.
Karkat wrapped his arms around himself, not saying anything.
Dave sighed and looked at his feet "look, you should eat something. You've lost so much weight..."
Karkat looked at the area of the floor next to him "If I eat anything then I might just get sick.. I don't feel hungry... If I was then I would eat something..." Karkat sighed and curled up on himself
Dave frowned, looking away. He was quiet for a moment before he looked back to Karkat "Will you please just try...?"
Karkat swallowed hard. He wanted to please Dave... He really did... Karkat let out a breath and nodded slowly.
Dave smiled softly and got up. He helped the small troll boy to stand up as well.
Dave attempted to walk towards the door.

Keyword is: Attempted

"Dave, you're about to-" the troll boy started to say, but the blonde still tripped over Karkat's husktop. He groaned when he fell flat on his face.
Karkat stood over the strider "Are you okay...?" Dave groaned again and nodded, shifting so he was laying on his back.
The blonde reached into his pocket where his glasses were.
Dave's eyes widened "Fuck!" He pulled the snapped frames out of his pocket.
Dave groaned for the third time "Fuck, fuck, fuck, fuck! No!" Karkat took a step back, too used to troll emotions, expecting Dave to get mad and possibly hurt Karkat. Dave noticed Karkat's step backwards. He frowned "it's okay Karkitty, I won't hurt you. It's just..." Dave sighed and stood up "it's just that people tease me for my eyes but... The people here are our friends and I know they won't tease me.. Come on, let's get you some food"
Karkat slowly edged towards Dave, not really saying anything about what Dave had just said. "I think should lead.." He mumbled. Dave nodded "I think so too"

And so the smaller of the two boys led Dave out of his room and to the kitchen area