SUBREDDIT: r/relationships
TITLE: Am I [16/M] too into the Relationship with my Girlfriend [16/F]?
POST: Hey guys, sorry to plague this subreddit with your stereotypical teenage questions, but I honestly can't stop thinking/worrying about this question. 

Things got serious a few weeks ago. We started hanging out, kissing, so on and so forth. Whenever we're together, I just feel incredibly happy, like I don't have a care in the world. There's just nothing that compares to the feeling I get when holding her and we talk. We hang out once a week on the weekends since I have practice during the week, and as soon as we part ways I start longing for the next weekend to come around. 

Don't take this the wrong way, I definitely don't mean any of this on a creepy level. Rereading what I just typed, I realize that could come off in a creepy/obsessive kind of way. I truly just enjoy her company and the time we spend together. 

I wish we could see each other more often, as I only see her once in the halls all day, but I don't want to come off too strong, or her too think that I'm being weird/obsessive by wanting to spend more time together. I feel like we both have other friends that we should be spending time with, and that if I ask to hang out more than once a weekend she'll think I'm being clingy. 

I guess what I'm asking is, am I overstepping a line here? Would asking her to hang out more often be like an invasion of space? Would it come off as needy/clingy? Once the spring season ends, would asking to hangout someday during the week come off in a similar way? 

I should probably mention this is the first serious relationship I've had, and that she made the first moves to start it. Thank you so much!
TL;DR: 
I want to spend more time with my girlfriend, does this come off as clingy, needy, or an invasion of space?