Yes a C will weight you down, thank you stupid 5 hour calc for engineers class in my freshman year!
The way that it will weight you down is the GPA screen. Many/most schools screen applications before they read anything, as long as you clear the screen, it won't matter much. This is so they're not reading apps on 3.0 gpa 24 mcat candidates.
Without the C I'd have been competitive (gpa-wise) at the top schools. With the C, still competitive at most schools and was accepted at my top choice.
You'll be fine as long as you choose schools that are seeking candidates w/MCAT, GPA, etc similar to yours, all this is published in MSAR.
Unfortunately there are no absolutes in the app process, all else equal, higher grades are always better than lower, ditto for MCAT, ditto for more clinical hours, volunteering, research, well connected relatives, etc. Just shoot for the best you can and keep strengthening your app!