Most likely your ancestor was helping king George to put down the rabble rousing scum in North America while fighting under the flag of Hesse-Cassel and in his native uniform. If it indeed wasn't 1775 but the early 1800s the reason likely was French occupation. Hesse-Cassel did not cooperate with Napoleon and was subjected to a military rule. In the Hesse dialect there still is the expression "and don't you make any visitez-ma-tente!" which a mother tells to her more supple daughers going out for a walk.