"your sticking at the supposed labor or cost of a godly life"
I think sticking at here is meant in the sense "To scruple at; to hesitate to accept or believe, to demur to, take exception to, be deterred by" (OED, stick v.1, PV2.1 to stick at) or "To be impeded or brought to a stand at (a difficulty)" (ibid., PV2.2). This sermon was written by Richard Baxter, a non-conformist; one of the OED's citations is to his fellow non-conformist John Bunyan, who wrote in The heavenly foot-man (1688):
They who will have heaven must not stick at any difficulties they meet with, but press, crowd, and thrust through all that may stand between heaven and their souls.
Likewise here, the people being addressed in the sermon are said to be deterred or hindered by the supposed labor or cost of a godly life. That is, they are reluctant to lead a godly life because they perceive it as being too difficult or costly. They have "cold and lazy prayers and performances" and continually give in to their temptations. Baxter calls on his audience:
The next time you go prayerless to bed, or about your business, conscience might cry out, Dost thou set no more by Christ and thy salvation?
He believes the labor and cost to be worthwhile, in view of the reward.