Unix PDP-11 assembly, 18 bytes binary, 67 bytes source
(this is becoming a theme with me, maybe because it's the only language I sort of know that no-one else here does.)
inc(r0)
Increments the single byte addressed by the initial value of r0 [which happens to be 05162 according to the simh debugger] as of program start.
0000000 000407 000002 000000 000000 000000 000000 000000 000000
0000020 005210 000000
And, as always, the extraneous bytes at the end can be removed with strip.
I made a few attempts to get the source shorter, but always ended up getting either a syntax error or SIGBUS.