Hi Margaret,
I can't help you specifically with this one but I too am looking at Borthwicks (my mother's maiden name) in that approximate area. A wee bit more northerly - Whitekirk / Dirleton in late 18th early 19th century, then to Dalkeith.
I've no doubt you are aware how common the name is on that East Coast area but you never know, we may have a link.
Feel free to have a look at my site - the Borthwicks I've positively identified as my rellies are on there.
I'll check through other stuff I have too in case there is anything that might help you.
I'm stuck on Peter born circa 1795 - have you ever come across him?
PS Welcome to Rootschat. It's a brilliant forum.
Dave