Pete Davidson Turning a Corner On Mental Health Issues

2:35 PM PT -- We're told the tweet Ariana posted -- and then deleted -- that set him off was, "stop weaponizing mental health. everyone." She was responding to Kanye, who had called her out for inserting herself in his beef with Drake. We're told after Pete saw Ariana's tweet, that triggered him to respond with a post supporting Kanye, followed by his suicide threat.

Pete Davidson is turning over a new leaf thanks to the immense support of his loved ones ... and he's getting professional help as well.

Sources close to the 'SNL' star tell TMZ ... he's now hunkering down and focusing on his mental health issues and his well-being. We're told friends and family members rallied around him this week, and calls of support and encouragement have been coming in nonstop.

Our sources say Pete's been overwhelmed by all the love and it's lifted his spirits ... and he plans to be back on 'SNL' when it returns in mid-January.

We broke the story ... Davidson was really in a dark place last weekend when he posted an ominous note suggesting he wanted to die, and he even believed his friends and colleagues didn't care about him. We're told what spun him into that dark place was Ariana Grande's tweet seemingly making fun of mental health issues.

Pete now realizes ... his friends and family do indeed care about him ... a lot.

As for his ex-fiance, Ariana Grande, being turned away by security when she rushed to comfort him ... we're told it's because he was hurt by what she tweeted.