Looks like a bug:
from https://launchpad.net/~ubuntu-mate-dev/+archive/ubuntu/xenial-mate:
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… The version of MATE 1.14 in this PPA is built against GTK2+ …
however:
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$ ldd libmateweather.so.1.6.9 | grep gtk
libgtk-3.so.0 => /usr/lib/x86_64-linux-gnu/libgtk-3.so.0 (0x00007f0515a6d000)
I am not completely sure but possible solution (until they make a new version) could be to replace the /usr/lib/x86_64-linux-gnu/libmateweather.so.1.6.9 with file from the previous version (1.14.1-1~xenial1.1). This version is built against GTK2+ and works. I know this because I have another machine where Mate Xenial was installed several days ago.