This is the Anguilla weather I know and love.
From 2002-2007 we would spend at least a week in March in Anguilla.
For the first time in 2008 my Dad and I swapped our traditional weather in March for February's.

Shoal Bay, March
To be honest, it is a little chillier in February (I would wear a light sweater at night!).
March, on the other hand, is ideal...
Average High in March: 84°F
Average Low in March: 73°F
Average Temp. in March: 78°F
Average Rain in March: 1"
The days are warm, but not yet hot, and the nights are warmer still. I could leave my sweaters at home! ;-) Friends who live here year-round though, still do wear long sleeves once the sun goes down.
For those five years (2002-2007), we would alternate between our favorite Anguilla villa on Shoal Bay and our friend's old place on Barnes Bay. I always took note of the ocean. The waters get calmer in March, but Dad would still find it tough to float in the seas at Barnes and Shoal!
I might be biased for my years of fond memories associated with weather in March, but this is my favorite time of year to be in Anguilla.
Anguilla travel tip: I know I said I would leave my sweaters at home, but, on second thought, I would pack one just in case, you never know... :-)