There are tons of algorithms that can generate a one-byte checksum. Algorithms include:

1. Checksums: add up all the bytes (or some permutation of the bytes) and perhaps perturb the result
2. CRC: calculate an 8-bit CRC, or some bigger CRC and drop all but 8 bits of the value.
3. XOR: take the XOR of all values, potentially with a rotation in between each byte
4. Linear congruential generators: Each step, multiply your seed with one prime, and add the value of the next byte
5. Any other hash function, where you end up dropping all but 8 bits (or 7 bits, even.)

Without the source code of the application, you have to make guesses about what could be going on, and verify those guesses against that data that you have. Sometimes, writing code that tests various parameters against various algorithms and sees how close it can get may be helpful. There really is no "magic bullet" here.

To get you started: If you start with the first value (0x7D) and subtract all the other values, you get 0x10. Do you get that same result for all other data packets you have? If so, you have the algorithm there.