Ah ok, an Arachnoid cyst. FWIW, children with those have been on growth hormone treatment, some because the tumor was pressing in the pineal gland causing growth hormone deficiency, and a connection between growth hormone and the growth of those was never found.
Whether and how much they grow appears dependent on how well fluid can or can't drain from them. Unfortunately, you'll have to keep an eye on it, but, at least in normal therapeutic doses, HGH doesn't have an impact on its growth like it does on cancerous tumors. Since HGH can, in rare cases cause an increase in pressure on the brain though, it may go from no-symptoms to developing them if squeezed against some structure by the added pressure.
BTW, they can also be caused by head trauma, if you had any.