I don't believe it was ever a hotel or restaurant because the deeds always mention it as being a parsonage. Anything is possible, but I'm basing this on my research of plans, deeds, and mortgages I could find online with Belknap County.
The Methodist used to (and still do in some areas) have circuits they travel each year or each summer, as was the case with this group in the Weirs. The parsonage is generally where the "big wigs" would stay. This area is part of the Methodist Circle that McDude refers to in his wonderful thread about the history of Weirs Beach.
There is mention of the large flue you're wondering about in some of the early deeds - as far back as 1947 - but the place is still called a "parsonage". Since the place was probably used the most in the summer and there was no air conditioning, the next best thing would be a vent (flue) from the kitchen. That's not an uncommon feature in many 'institutional' kitchens from that era.
Hope this makes sense.
