As a native Jersey guy, I should have known where Howell is, but somehow I forgot. Monmouth county is actually pretty flat. I wasn't sure if you were in the hillier part of NJ but you are near the coast so there really aren't big hills to worry about. So the good news is, the stock gearing on most road bikes should be OK for you to get started.

OK, re: bike weight. On flat or downhill, bike weight is not really a factor except when accelerating from a stop. A road bike puts your body in a more aerodynamic position (if you have the core strength and flexibility to do it) and that makes a difference in speed vs. perceived effort. Also, road bikes are designed to be very stiff laterally so your pedaling motion translates into forward motion rather than in frame flex.

And while bike weight is a factor going uphill, it isn't as much of factor as you would think. Since you weigh over 200 lbs, the difference between climbing with a 20 lb road bike and a 28 lb hybrid is 220 lbs vs. 228 lbs. a 190 lb rider riding a 30 lb bike is pulling the same total weight uphill as a 200 lb rider on a 20 lb bike. Except for pro racers who are all extremely lean, most recreational riders would get more benefit from losing 5 or 10 lbs than they would by buying a lighter bike.

If you are having trouble going up grades, that is more a matter of fitness than it is a question of bikes. Since you just got started, you probably need to give yourself a break and keep working on your fitness and climbing technique. Some folks make the mistake of trying to "power through" hills when what they need to do is keep their cadence high. If you are going that, shift down to a lower gear and trying spinning, rather than hammering up hills. It is better for your knees and a better way to climb hills. If you watch any professional road race, you will notice that is how most of the pros climb these days. If you do this enough, the hills will get a little easier and you might even look forward to conquering them or at the very least, you won't fear them.