it's not weird at all and is considered by most a more modern/stylish way to wear a suit...
though technically it's not a suit anymore...it's separates...
but it still works and is still perfectly acceptable...
at least for women...
although if you were going somewhere like court, i might say that you should wear a more traditional style suit...
for men i'd say you should still match top and bottom for more serious situations...but you can mix a sports jacket and pants for less formal ones...