By default, the delete character (ASCII 127, ^?) acts as the interrupt key (usually bound to ^C on more modern Unix-like systems). Pressing the interrupt key will behave as you describe. In Unix v7 there's no easy way to change this except to modify the kernel.
If your terminal sends a delete character when you press the backspace key, try modifying your terminal settings so that it sends backspace (ASCII 8, ^H) instead. Then use the following command to get Unix to recognize backspace as the erase character:
stty erase '^H'
While you're at it, you might want to also set the line-kill key according to modern usage:
stty kill '^U'