I applied to a NASA internship for the spring semester, and I want to reapply for the internship for summer. Is it okay and good to ask the same professor who sent a recommendation letter for my spring application to resend the same letter for my new summer application? Does it weaken my application in any way?
Yes, that's perfectly acceptable. I've submitted duplicate letters myself in support of reappointments for some of my students and they've all been successful. (But like most instructors, I only agree to write an LOR if I can write a good one that I think will be helpful.) The only reason for concern would be if you were turned down on your previous application and you worry it might have been because he/she gave you a weak reference.