My name is both long and unusual, and apart from a short period of my life when I was desperate to have a nickname (teenagers!) everyone except my immediate family call me by my full name (my family on the other hand rarely use my full name, and my mother has a nickname for me too). I do get double takes and have to spell it, and people often mispronounce it too, but then I also get a lot of "what a nice name" "where does it come from etc", and once people have got the hang of it they don't forget it. On balance I am very happy with my name (although I didn't give either of mp children very unusual names).
I agree with some others that people do need to have a new and different sounding name said to them several times before they get the hang of it, and will ask about where it came from. That's not rude, just interested. You just need to get your "patter" going - to be honest I'd just say that it's traditional in your dh's country, and not go into much more detail, just because it's a bit too much (in my case I can tell people how my parents chose my name, that it's in a tradition that has now mostly disappeared, the french name it's based on etc etc, but mostly I just say that it is English, and that my parents had unusual taste, because generally people aren't really that interested ).
I wonder with your family if there isn't a more simple explanation, that is that it is a long and formal name, and perhaps just seems too much for a very tiny baby? Most children pick up a diminutive or two along the way, they usually are quite transient, and given in love, so I'd not worry too much. Of course if you really dislike "Wee-T", then you will need to ask your brother to desist (it does sound quite cute though )