Once upon a time, almost all cars were constructed with a steel frame to which one attached a suspension, drive train, steering gear, and a body.
Since everything else in all models in a range was essentially the same, weight depended on the body. A lighter body could mean better acceleration both in a straight line and centripetally (changing direction).
Thus it became axiomatic that a touring car (without the weight of a solid roof) was faster than a town car, a coupe (dispensing with the weight of two doors) could outrun a sedan, a convertible had the advantage over a coupe, and roadsters (with no top at all) had them all beat. Thus was born the perception that topless motoring was sportier than other alternatives.
But nearly all cars now are of “unibody” construction, meaning the body is the frame. This is a terrifically efficient type of construction, allowing great strength for safety, and stiffness to provide a stable structure on which the suspension can work.
Of course, the roof of these cars is part of that structure, and the distance between the floor and the roof increases the section modulus (like the two flanges of an I-beam) enhancing its efficiency still further.
You can see where this is going, right? Make a convertible out of a unibody coupe and you cut the top flange off your I-beam.
If you’re not to end up with a limp chassis that wobbles and flutters at the slightest ripple in the road, you need to add structure. Since your section modulus is reduced to that provided by the depth of the rocker panels and floor tunnel, you need a lot more of it, adding weight. If instead of a cloth top, you add a retractable roof and its mechanism, your weight penalty is redoubled.
Because some of the operating mechanism for the convertible or retractable top stores in the space between the rear seats and the fender panels, rear hip and shoulder room is reduced, and in a retractable you also reduce available luggage space to near zero.
Convertibles have their charms, of course. It’s great to cruise with the sun on your face and the wind in your hair, but how often will you really do that?
I once checked out all the convertibles I saw on a mild sunny Southern California day, and more than half of them had their tops up. If you are not going to put your top down on a day like that, when are you? I got up the nerve to ask the question while stopped at a light, and all I got was embarrassed laughter.
So if you are ever in the position of having the choice between a car with a real roof and one without, go for it. When you do though, at least know what you are getting into, and what you are not.