I didn't know there had been a barracks at Weeley until I started transcribing the Weeley parish registers. There were so many babies born at the barracks (which at one point had more people living in it than in Weeley itself!) that they had their own maternity ward, in effect!
My transcriptions are on
www.FreeREG.org.uk so if you think your family may have been stationed there, it might be worth searching.
I'm putting together a new website (I used to put my transcriptions on my own site but now they're all on FreeREG) where I will have surname lists (so a surname index, basically) by event in each parish. Not sure when that'll be finished though!
It's very interesting though as you can see local girls marrying the Scottish soldiers (there were a LOT of Scottish Highland regiments passing through Weeley), and there's also lots of illegitimate babies produced by local girls, given Scottish-sounding middle names! Plus you had various militia there - Essex and Surrey, being ones I recall.
There's a book on Google Books which is a compilation of letters written by an officer's wife. She lived at Weeley for a while and she talks about the horrible living conditions - they lived in wooden huts and there were huge amounts of mud whenever it rained, but she talks in amused tones about it, and I suppose she was quite glad that she was able to spend time with her husband, rather than have him stationed overseas while she was stuck in the UK (I think this may explain all those aforementioned babies!).