"Die Frau ist größer."
Why can't it be 'the wife is taller' or 'the woman is bigger'? Taller and bigger seem interchangeable - is that right?
I don't think bigger and taller are interchangeable at all. If I say my wife is "größer", am I saying she is taller or am I sleeping on the sofa?
In general, 'größer' can mean 'bigger' and 'larger' as well. But when talking to your wife (or any other member of the homo species), it definitely means 'taller'. If you want to sleep on the couch use 'breiter' or 'dicker' ;-)