AVR USART wait for AVR's reponse to continue text stream
What you need is "flow control" or "handshaking".

For USART, you can use hardware flow control with RTS/CTS, but many USART implementations today omit them. If you've finished you hardware and without these pins connected, you may try "software flow control" with "XON/XOFF", because these two codes won't appear in your text file (they are non-printable character). So use them as flow control is possible. But compared to hardware flow control, the later may be a little slower.

The main limitation with you it's your MCU is not strong enough to handle the entire file, so parse the file on PC end is reasonable. 

If you don't want to dive into a complicated USART programm on PC, you can try Tera Term, an open-source, programmable, handy "Hyperterminal" killer.