Welcome to the Twig search Baird
unfortunately so far I have no Henry.....

But I have a Michael in Belfast 1760-1800 a cotten thread/muslin merchant with links to Manchester.
I have also found that lots of Twig;s are either, born ,marry ,have children ,then die and the spellings can change each time.
Twig Twigg Twiggs Twigge Quid Quigg Tuig Tuigg to name a few
I have followed many families backwards to find them go from Twig to Quig and back to Twig again ( think it is the Irish pronunciation)
I will keep Henry in mind and let you know post haste if I find him ...do you know of any other family names or his fathers name?
Steve