Girlfriend is (legitimately) busy, but I don't like the frame it creates

Dear all,

So I have this girlfriend, we're going on a year soon. The problem is she is very busy which kind of creates the frame of me being the one who wants to see her more (even if that's not necessary the case).

She's waiting tables most days from ten in the morning until 11:30pm-midnight, or until the last restaurant guests leave (which can sometimes be late). And she has a four year old son from a prior relationship.

The day before yesterday she wanted to introduce me to her mom, so we all went out for dinner together. Afterwards she came home with me. The next morning she says "I'll come see you after work today". And she did come see me, but she didn't get off work until 1am and was only able to stay a very short while before going home (had to take her kid to kindergarten next morning).

When she got home she texts me:
She: Are you happy together with me?
Me: Yes
Me: Why are you asking? Are you happy together with me?
She: Yes, I am happy together with you. But I'm not happy with myself. You devote time to me, and I'm always tired or busy.
She: I run between my home, the restaurant and your apartment, but it's hard to find enough time.
Me: What do you want to do about that?
She: I don't know. What do you want me to do about that?
Me: Be with me
She: I will be with you. I love you.

Gentlemen, I don't know. She obviously tries to fit me in to her busy schedule and she wanted me to meet her mom (and son) so she is serious about me. And this day she was the one who said (uninvited, although she doesn't need an invitation obviously) that she would come to my apartment after work. On the other hand, when she feels bad for not having enough time to spend with me, I feel that it creates a very unfortunate frame in which I'm the one doing the "chasing" (even though she's my girlfriend).

1) How do I handle this without being the needy guy who's always ready to see her whenever she has time for me, while also not ending up almost never seeing her? Do I just be cool and understanding about it?

2) I'm rather successful professionally and earn quite well - in theory I could easily give her an equal amount to her salary each month for her to not wait tables. That way she would get to spend more time with her son, chase her dreams and of course spend more time with me. I'm not sure if this is a good idea though?

Looking forward to hearing your input on this, gentlemen.

Oh, and also, I'm in my early thirties, been following this forum for more than ten years and have become quite successful with women (if that would be of any relevance at all...)