Why can't it be 'the wife is taller' or 'the woman is bigger'? Taller and bigger seem interchangeable - is that right?
Got me too
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' ;-)
Die Frau ist alter?
No. 'älter' (note the Umlaut) means 'older'.
Of course. Apologies, I was getting confused with Spanish (alto/alta = tall)!