The versions I compile (including the Windows TeXLive version) always include support for GSL, but the TeXLive group is hesitant to require dependencies that are missing on many of their UNIX build platforms. But feel free to ask them to include GSL in the future. A precompiled linux (Fedora 23) version of asy can be found here: https://sourceforge.net/projects/asymptote/files/2.41/asymptote-2.41.i386.tgz/download which may work for you if you have all of the libraries installed. There is also an...
You simply need to address that error message: install libreadline version 6.3 from https://ftp.gnu.org/gnu/readline/ Alternatively, if you prefer to use readline version 7.0 just compile Asymptote on your machine (rather than using a precompiled version built with a different library configuration).
Did you try checking out and installing in a new directory?
tlmgr install asymptote is for TeXLive, nothing to do with MacPorts. Asymptote is installed automatically when you download TeXLive from https://tug.org/texlive/ But if you want to use MacPorts, you need to follow these instructions: https://www.macports.org/install.php Then you need to port install asymptote It's up to you which method to use, but since you need to install TeX anyway, maybe the first way is easier for you.
If you are trying to compile from source you need to download asymptote-x.xx.src.tgz But if you aren't used to that it, it might be easier for you to install a precompiled Asymptote binary from http://www.macports.org/
I think you just need to do a make clean and then try again.
A better solution is for WinEdt to check for the warning LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. and rerun pdflatex again if needed.