Be careful: you must NOT change these macros inside curlbuild.h
! This header is generated at configure time and it records (among other things) which architecture is targeted.
If you look at the pre-built static library provided by BBHTTP you can see that it only targets ARMv7
and ARMv7s
architectures:
$ otool -fV External/libcurl.iOS/libcurl.iOS.appstore.a | grep Archive
Archive : External/libcurl.iOS/libcurl.iOS.appstore.a (architecture armv7)
Archive : External/libcurl.iOS/libcurl.iOS.appstore.a (architecture armv7s)
These are 32-bit architectures. Please refer to BBHTTP Dependencies for more details regarding how this static library has been compiled.
If you build an iOS app with iOS 7 as deployment target you certainly have the default archs configured within your build settings. And these defaults include a 32-bit slice, plus a 64-bit slice:

So in such a case you must include a libcurl fat static library that also contains a 64-bit slice (a.k.a arm64
).
The curl iOS build scripts from BBHTTP's author might help you. Otherwise please refer to Nick Zitzmann libcurl pre-built.