Short arms, deep/long pockets

This expression is a jocular metaphor for someone who is disinclined to spend their money when called upon to do so e.g. in buying a round of drinks etc. It is originally American and is first cited from the early 1950s. It is thought to derive from an earlier American expression 'deep pockets' (without reference to 'arms') that dates from the 1940s, meaning pretty much the same thing.