Is he asking you out on a date, or is he asking for a relationship with you? I'm still in high school, but from my point of view, there's no harm in going on a date with him. Maybe you can then see if he's right for you and decide whether or not you want a relationship.
I suggest you do whatever you want. And I'm guessing you're not super excited about this.
I don't know you, but based on your reaction, I'm guessing he likes you more than you like him. I'm guessing if you had strong feelings for him, you'd be super excited that he finally asked you out after waiting three whole weeks. (My husband asked me out after only knowing me for one week, and even that felt like forever.)
You have every right to say no...even if he seems like a nice guy. If he's not your type, then that's fine. You don't owe him an explanation or a date.
If you wanna try it out, make sure he knows it. Don't just say yes, because that can be taken different ways. Just ask him if he's ok with you two just hanging out and testing the waters. It sounds indecisive maybe but if you guys realize you don't click later it'd be a little less awkward maybe.
I'd say that you should date him/go out with, if you are interested in him. It's too soon to tell what he wants from you or how he sees things from his perspective, the only clear thing is that he is interested, but beware, he might also be a jerk and play with your feelings. You are young, don't worry about the age difference. You are probably nervous about experiencing something new, but thing is, you won't know how it is to date/be in a relationship unless you start letting yourself go there. As latter, you are young, you should go for it. And it doesn't even have to be a date, you can go out as friends, if it makes you feel more comfortable.
If you feel like you could be attracted to him physically then go out with him and get to know him. If the thought of being physical with him makes you awkward and uncomfortable then you should probably just be friends.