You're tall, but you're still light... but you're not gonna get any lighter. Think ahead with your next board.
If it sinks when you're paddling or sitting in the lineup, you need more volume overall. If it sinks when you're riding, you need more planing surface. If your local breaks are usually softer (I haven't surfed in Wildwood in many years), you're gonna want a little extra volume. You could go up in length... 6'2 - 6'6... or you could go wider... a lot wider... like 19 - 19.5... or thicker... maybe 2 5/8.... or some combination of those, basically scaling the whole thing up. If you surf more punchy waves, don't go that wide... keep it under 19. But the trend right now is wider... and it works. I personally prefer to not go up too much in thickness for a shortboard because it changes the flex/feel. I like to go up 1/8 or so and foil the whole thing a little thicker, not just ball up volume in the middle.
Not sure why your board sinks. I am 5'10", 185 pounds, and ride a 6'2" x 18 5/8 x 2 3/8. Its on the low side of the volume I require, but I surf it just fine in knee high to well overhead. I'm 32, and an average to intermediate surfer. Not someone trying to prove anything with a tiny potato chip board.
You're board should have more than enough floatation for you. I'm assuming you are young, based on your height to weight ratio. You are probably used to it floating you like a longboard would, as I'm guessing you used to be smaller.
If you are dead set on looking for something new, and not just adjusting to your new size (because that board would float me, and I have 40 pounds on you), I would recommend a few things. Talk with a local shop owner, and have him find you a board that is in the same size range, but is more geared for the area (I'm from Cape May, I know the breaks in our area well). I would go with a similar sized board, but with full rails, low entry rocker, and some extra width in the nose and tail. If you find a board with that shape in mind, you might even be able to move to a "smaller" board.
If you are interested, I have two boards I had custom shaped for me back when I was in college. They are still in great shape. One is a 6'1" x 18 1/2 x 2 1/4, and the other is a 6'3" x 18 3/4 x 2 3/8. They are by East Coast shapers, full rails, low rocker, wider in the nose and tail.
Let me know if you are interested in either one.
Also, PM me if you don't know much about board design, and why the low entry rocker/wider nose and tail, etc. will help you. Would be happy to help you out.
Good advice from fins. I'm always tempted to say things like, "that board should float you. I ride a..." but the goal is to get what's right for YOU. If you don't like the way your board floats you, good on you for knowing what you want. Too many guys don't...
A word on rocker... If you like the rocker on your current board, going flatter will change how the board drops in and turns in the pocket. It will give you more speed through flat sections, but it won't ride the same in the steep, curvy part of the wave. Rocker and volume are different elements of design. If you're only concerned with float, and you like the way the board performs otherwise, stick with the rocker you're used to and adjust the volume.
Also... be conscious of going longer and wider, but thinner. You might not be getting the change in volume you're after. Look at the overall foil of the board... both from nose to tail, and rail to rail. Fuller rails, flatter deck, and thickness that carries out to the ends of the board all translate into increased volume and float.