Is he too cheap? Should I be cautious?

I met this guy online and we met up for coffee and I insisted that I pay for the both of us. No big deal, it was the first date right? The date went ok and we decided to meet up again the following week. We meet to get coffee again. It's time to pay. My date stands there looking around the room. The cashier is waiting. So I pay for coffee again. I'm ok with getting it but he was the one who invited me so I thought he was going to pay. He even adds "Finee i'lll let you pay since you're so insistent on it." Um ok..
The next week he suggests going out for a movie. I agree. He recommends the dollar movie theater 35 minutes away from my house. There's another one 12 minutes away from my house but he insists that there is a movie at the dollar one that he wants to see. I go because he offers to pick me up and drive. We get there and it's time to pay, and he acts so chivalrous, blocking my still body so he can pay the two dollars for the movie. Afterwords we go for boba and once again he lets me get the $9 for the both of us.
Not only that but for dates he always wants to "walk around" or go to places where we don't have to spend money. Since we're both in college and busy with school, we only meet like once in 2 weeks. He has never offered to take me to dinner/lunch yet. Most of the time, he texts so we can hang out in the library.
I don't mean to sound so shallow but sometimes it would feel nice to be wined and dine by my date. I mean it would be nice if even if he offered to do so. Sometimes it feels like he's trying to be really cheap with me. But I never tell him how I feel because I don't want to make him feel bad or sound shallow.

Should I tell him? Or am I just being shallow?
Is he too cheap? Should I be cautious?
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