#x86 machine code, 9 7 bytes

D1 E9 SHR CX, 1 ; divide length in half AD LODSW ; load next two chars into AH/AL 3A E0 CMP AH, AL ; compare AH and AL E1 FB LOOPE -5 ; if equal, continue loop 

Input string in SI, input string length in CX. Output ZF if is double speak.

###Or 14 bytes as a complete PC DOS executable:###

###Original 24 bytes complete PC DOS executable:###

###Credits:###

x86 machine code, 9 8 bytes

D1 E9 SHR CX, 1 ; divide length in half  L1: AD LODSW ; load next two chars into AH/AL 3A E0 CMP AH, AL ; compare AH and AL E1 FB LOOPE L1 ; if equal, continue loop C3 RET ; return to caller 

Callable function. Input string in SI, input string length in CX. Output ZF if is double speak.

Or 14 bytes as a complete PC DOS executable:

Original 24 bytes complete PC DOS executable:

Credits:

B4 01 MOV AH, 01H ; DOS read char from STDIN (with echo) CD 21 INT 21H ; read second char into AL 92 XCHG DX, AX ; put first char into DL B4 08 MOV AH, 08H ; DOS read char from STDIN (no echo) CD 21 INT 21H ; read char into AL 3A C2 CMP AL, DL ; compare first and second char 74 F3 JE -13 ; if the same, continue loop C3 RET ; otherwise exit to DOS 

B4 01 MOV AH, 01H ; DOS read char from STDIN (with echo) CD 21 INT 21H ; read first char into AL 92 XCHG DX, AX ; put first char into DL B4 08 MOV AH, 08H ; DOS read char from STDIN (no echo) CD 21 INT 21H ; read second char into AL 3A C2 CMP AL, DL ; compare first and second char 74 F3 JE -13 ; if the same, continue loop C3 RET ; otherwise exit to DOS 

-2 bytes thx to @ErikF!

Or 9 bytes:

D1 E9 SHR CX, 1 ; divide length in half 8B FE MOV DI, SI ; string pointer to DI 47 INC DI ; offset DI by 1 byte A6 CMPSB ; advance SI and DI (ignore comparison) A6 CMPSB ; compare [SI] and [DI] E1 FC LOOPE -4 ; if equal, continue loop 

Unfortunately can't use REPE CMPSB since it will only advance SI and DI by one byte on each iteration.

Or 26 24 bytes as a complete DOS executable:

(will re-do screenshot with new program size when I have more time)

Build and test ISDBL.COM using xxd -r:

###Or 14 bytes as a complete PC DOS executable:###

B4 01 MOV AH, 01H ; DOS read char from STDIN (with echo)  CD 21 INT 21H   ; read second char into AL 92 XCHG DX, AX ; put first char into DL B4 08   MOV AH, 08H ; DOS read char from STDIN (no echo)  CD 21 INT 21H  ; read char into AL 3A C2  CMP AL, DL ; compare first and second char  74 F3 JE  -13 ; if the same, continue loop  C3 RET ; otherwise exit to DOS 

Input is via STDIN, either pipe or interactive. Will echo the "de-doubled" input until a non-doubled character is detected, at which point will exit (maybe bending I/O rules a little bit, but this is just a bonus answer).

Build and test ISDBL2.COM using xxd -r:

00000000: b401 cd21 92b4 08cd 213a c274 f3c3 ...!....!:.t.. 

###Original 24 bytes complete PC DOS executable:###

Build and test ISDBL.COM using xxd -r:

###Credits:###

• -2 bytes thx to @ErikF!