Hi, AliB,
Frank II and Lola are correct. If you are flying BA from GLA to LHR, then taking a connecting BA flight back to the US, you only go through security at Glasgow, which I have to say is a hell of a lot easier and more pleasant than going through security at Heathrow.
You should make sure that you have at least 90 minutes between your arrival time in Heathrow and your departure time to the US. If you are making the transAtlantic portion of your journey on a non-BA airline, give yourselves 2 1/2 hours.
Sometimes it doesn't make a difference. Last July, our flight from GLA to LHR was delayed by two hours, resulting in our missing our connecting flight to PHL. Fortunately, we were able to get the last two seats on a later flight to BWI, so at least we were able to get home the same day. But it was a 17 hour day from GLA to BWI, so we were completely knackered by the time we arrived home. :(
Not to worry - BA are really good about getting you to your destination!
Best wishes and good luck!
Mike (Auchterless)