Here's an update. I just received a copy of the Birth Certificate of one of his sons, who was born in 1918. It says that Robert Tweedie was a gunner in the Royal Field Artillery. This would be, I assume, the 35th Brigade which was the Glasgow Division.
I need to ask my grandfather if he was one of the 'Bantams', that is, men who were under the regulation height of 5 feet 3 inches! His son, my great grandfather was six feet tall as is my grandfather so that would be surprising. I'm thinking he may be one of the recruits from after 1916 when that wasn't allowed anymore.