A hearty Florida welcome to you--great site here. Yep--your dealer was right on. Without about 40 lbs of additional gear, the OB will feel "tippy." My 135 lb brother-in-law was wobbling all over the place in the OB. Even I, at 175 lbs, have felt the same in the OB on occasion with no gear aboard. Of course, you would probably get used to it over time and not notice it all that much, but I think the Sport would be perfect for you, depending on your inseam length. I am 5'11 with a 30 inch inseam, and the "throw" of the Mirage drive adjustment has to be set as far forward as possible for me. But in the OB, I can set it about in the middle and am comfortable.
But, as mattyak and others point out you need a fair amount of weight to set the OB down on its haunches (or sponsons = hull bulges). I was out with my buddy last weekend--I in the Sport and he in the OB. Now he is about 6'2", but tips the scales at a hefty 285 lbs, and I have to say, he really put my OB right down in the water with that weight. Yet he was perfectly comfortable, even though he had never been in a yak before, and was hesitant initially even to try because of his weight. However, the OB is "advertised" by Hobie to handle up to 450 lbs! That may be pushing it a bit, but 300 lbs or so is no problem for the OB.
As matt also points out, I have come around to using my wife's Sport more than my OB now. I had knee surgery last year, and although the knee is fine for normal walking, I do notice it when I have to lug around a heavy load. I weighed my OB with all the extra RAM balls, SS hardware and screws, rudder, etc. and it came in at 77 lbs on the bathroom scale. I have to say that I sure notice it with my knee and back, as compared with manhandling the much lighter Sport around on the ground.
It is interesting to me that JonS, who is one of the owners of KayakFishingStuff.com, and who can choose any yak made, has mentioned that the Sport has become his favorite yak for its maneuverabiity and handling, especially in freshwater. But, if you are traveling long distances on the open sea, or in bays and inlets, the Sport will probably be way too slow for you, and you will definitely have trouble (as in impossible!) keeping up with someone in a Kaskazi Dorado, Hobie Adventure, or a Tarpon 160. Speaking of which, you might want to look at a BigA (my name for the Adventure), since it has a much different hull design than the OB and does not have that tippy feeling for smaller folks.
Good luck with your choice, but you can't beat Greg Ketterman's Mirage Drive for all around use, and especially that hands-free maneuverability when fighting a fish, trolling, rigging a line, photography, etc.