You're overthinking this man. Don't look for her approval, you don't need it. Be confident and just tell her what you want - if you think she's hesitant to meet you can just straight up ask her. Don't waste your time being too nice.
Also, your message sucks. Just propose a plan. "Hey, what you doing this weekend?" pretty much means "Hey, I was too lazy of something fun to do together so can you please think of something and can I please join?" - if you instead say "Hey, you wanna go play a game of pool/go minigolfing/watch netflix/order pizza this weekend?" - it's way easier for her to say yes and it also makes it easier to gouge if she's interested. If she replies "Sorry I need to study" its pretty obvious shes not interested. If she really has to study but is interested she'll go "Aww that sounds fun, but I have to study" or maybe even propose another date.