make one's hand

— I have lately written to you, I would not advise you to wade any further in these maters, for it is to be thought that the French king indendeth to make his hand by favoring you in the attaining to the said marriage; which when he shall perceive that by your means he cannot get such things as he desireth, peradventure he shall show some change and alteration in the queen's affairs, whereof great inconvenience might ensue.