Our post office has a scale in the lobby. Whenever I've had a question about a heavy item, I'll put the item in the car and swing by the post office when I'm otherwise out (grocery run or the like) and check the weight. I'll often bring along a suitable box and put that on the scale at the same time (that cardboard can add up!). Because I save the bubble wrap that danged near everything comes in from Amazon and places like that, I don't usually worry much about the weight of the packing, but, if the weight is borderline, I'll toss a couple of ounces into my figure.
That may not be much helpful for folks who live in cities where the nearest post office is across town and "across town" is a half hour drive; but, if you live somewhere more intimate, it's something to remember. If your post office doesn't have a scale in the lobby, you can probably get help from one of the window clerks to get a weight estimate (but maybe not this month...the lines are already noticeably longer at my post office - people with overseas friends and family, I guess).
And, yes, an ounce can trip you up on postage rates.