We, too, have flown several times with various strollers in tow: from an umbrella, to a light-weight, to a double-tandem. Just a heads up: because the on-the-ground crew is under a time crunch, they are not always "careful" with items left for gate-check...especially if it's a heavy item. For example, our double stroller's cup holders were busted off twice, and
we had to replace them; and my sisters' jogger-type stroller's back wheel got bent. If you can remove any external pieces from your stroller, do, or better yet, get a stroller bag (you can find all sorts of sizes and prices online nowadays). Oh, and it doesn't hurt to label your stroller (we've used a luggage tag in the past).
When you get to your gate, ask the desk attendant for a "gate check slip." When it's time to board, it's easier, and nicer for the rest of the people around you, to have your stroller folded up before walking down the jetway. Then, you simply leave your item at the end of the jetway, right before you board the plane. After the plane lands, I like to wait until most of the guests have cleared before getting off the plane for two reasons: it gives me more room to maneuver my belongings and family down the aisle without disturbing others, and by the time we get off the plane, our gate-check item is there waiting for us and not the other way around

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Another food-for-thought, renting strollers off-site?

Because I like my DD3 to ride in her carseat on the plane (it's familiar and she's too tiny for the airline seat belts to fit properly), I prefer to just rent a stroller. By the time we arrive at our resort, the stroller is there waiting for us! And, it's one less piece of "stuff" to drag down with us!