You are correct in thinking that a caloric deficit over a period of time will result in weight loss. Don't listen to anyone else when they say it's more complicated than this because it's not. The only thing more complicated is how you manipulate your macros to reach a certain body composition. For example, if you don't eat protein, you will lose more weight via muscle loss, or if you don't eat carbs, you will lose relatively more fat via ketosis but the end result is the same...weight loss. I see what you're describing all the time...whether it is someone skinny person saying "I eat a lot but can't gain weight", or someone little overweight "I eat less now why am I not skinny yet". Usually, the most common mistake is, you don't ACTUALLY know how much you're eating. You also need to play around with your diet, everyone is a little different. Your ability to lose weight is technically determined by calories in vs calories out but how are you so sure that you're actually in a deficit without counting ? I made this mistake for a solid 3 years, trust me, it makes a huge difference. You're 200 lbs, so this mean your resting metabolic rate is somewhere around 2800-3000 calories (this number could be much lower if you don't have adequate muscle, so start lifting more often and dont lift "light"). Now, knowing this rate, in order to lose about half a lbs a week, you need to consume 2800-3000 minus 500-600 calories on a daily basis, so anywhere from 2000 to 2500 calories to be safe. Use myfitnesspal or a daily log and actually record the calories on everything you eat, are you ACTUALLY consistently eating around this many calories? And please don't fall into the trap of thinking you burn 400-500 calories from these cardio machines, its been proven time and time again that the numbers you observe from these machines are so far from the truth it's not even funny...should be illegalized.
Another big mistake that I see here is the excessive cardio that you do. You need to remember that more muscle equates to more calories burned and hence a higher metabolism. Combined with "light" weights, this is a recipe to lose muscle mass. If you lose muscle mass, your metabolism will slow down accordingly, and hence the amount of food you used to consume before hand, may now be too much in order to reach a deficit. Fix: start lifting weights consistently (not light but not too heavy just yet), stop doing cardio so much and if you are going to not stop doing this cardio, consume most of your calories around it.
So to sum up:
Actually count your calories, and make sure you consume less than the numbers I said above.
Start lifting weights more often and cardio less often. It's known that excessive cardio (keep in mind I mean low intensity cardio) will make you lose muscle mass and hence lower your metabolic rate, as a result you will need to consume even less calories than you used to.
Try to consume around a gram of protein per lbs of bodyweight in order to maximize protein synthesis and hence get a higher metabolic rate through building muscle, this will help you maintain a deficit easier.
Don't go too hard on the alcohol, beer can certainly mess with your fat burning hormones as alcohol is a known fat burning suppressant. Think about it, why does the term beer belly exist?