You're lucky you're so close to your family. My grandmother passed last week, but I can't feel sad about it because we only ever visited her every few months. Be happy that you can feel sad.
Aye. One of mine I only ever met as a little kid (though she died while I was an advlt... some blame falls on both of us, I suppose :shrug:). The other I saw a little bit as a child, as she was much closer geographically, and dealt with a bit more in my late teens, including living with her for a time. Unfortunately, I can't say her death was a loss to the world: she was just not a good person. The people she cultivated as 'friends' thought she was lovely... but in truth she was a shallow, self-centred, and manipulative (easy to conceal that sort of thing if you pick your marks and they're not around you all the time, but family is tougher

). I'm not after any sympathy from anyone, BTW.
So, Steptim, the upside of being upset is that you've got something to be upset about. I imagine you enjoyed the time you spent with them, and have plenty of good memories. Hold those in your mind, and feel blessed that you had a chance to know your great grandparents*

.
Spoiler *Since so many of them die before their great-grandchildren are even born :hehe:.
But really, there is NOTHING wimpy about grieving. At all. I really don't think your girlfriend is going to think less of you for having emotions.
An' if she does, she's probably not worth having :shrug:.