First of all, it doesn't really matter. Programs compiled with that option aren't meant for general distribution. They're meant to help you find the problem so you can fix it and then ship a correct version of your program without the debugging options enabled.
Second, half a megabyte is only big if you still distribute on floppy disks. Whether that's truly much space depends on how big your program was beforehand. Compress your program when you distribute it, and you'll probably hardly notice the difference.
Finally, to the crux of your question, yes, full debug mode makes your program bigger. It should be obvious that enabling that mode adds more code. It adds the code that does all the debug checking, such as checking for heap corruption, generating stack traces, catching the use of freed interfaces, logging errors to a file, and logging memory leaks. It also adds code to load and use the full-debug-mode DLL, and it changes any assembler functions to be written in plain Delphi instead.
The compiler option about debug information should have no effect. It controls whether debug information is included in the DCU files; that information is always excluded from the EXE files (unless you're talking about TD32 debug information, but you shouldn't enable that anyway since you're not using Turbo Debugger).
If your program is looking for the Libc unit, then you did more than turn of full debug mode. You somehow turned on Linux mode. You're not using Linux, so don't turn on that mode. If you're stuck, replace your copy of FastMM4Options.inc with the original version and start over.