Okay I've managed to find the problem quickly thanks to both of your input. Basically the content length I was using was completely inappropriate. I was just setting it to a huge value with no relation to the actual length of the body.

It was the kind of thing I was expecting might be the case. I ...

I'm having trouble sending a file from the ESP acting as a server, to a browser requesting the resource.

I'm using the SSL api and reading a file from an SD card and sending it to a client on request. Had good success sending HTTP header specifying html content which is displayed in browser ...

If you only need a single immutable file, theres also the option of letting the build embed it.
Example for a file called "what_time.raw":

/* embedded file */
extern uint8_t file_start[] asm("_binary_what_time_raw_start");
extern uint8_t file_end[] asm("_binary_what_time_raw_end");

component.mk ...