Long Bow or Recurve:
The draw weight is the amount of force, usually measured in pounds, required to pull the bowstring back to full draw. It will usually vary with the draw length, so you'll need to know not only the weight, but the length at which it was measured. For example, a bow that is rated at 30 lbs at 29" would theoretically mean that as you begin to draw the bow, you will experience increasing resistance or weight as you increase the draw back to your draw length. In this example, we are using 29 inches, so if you do not reach your optimum draw length consistently, you will have varying amounts of kinetic energy when you release the shot, thus resulting in inconsistent performance. Also, if you draw the bow more than your optimum length, you will have more kinetic energy stored up than usual. Again producing different results than expected. Here the key is consistency. With Long Bow or Recurve, you will need to be able to hold the bow draw weight long enough to aim and smoothly release your shot. The point here is that you should choose a bow draw weight that does not cause fatigue and "the shakes" or your performance will suffer.
The draw weight for compound bows is a little different because you have a peak draw weight and a let-off draw weight. The peak draw weight is how much resistance you must overcome to get the bow string to almost full draw. Somewhere around the 3/4 draw point, you will experience something called the let-off. The let-off is normally rated at some percentage. For example many modern bows are rated with a let-off as high as 80%. In other words, if you are drawing a compound bow that is rated at 70 pounds peak draw with an 80% let-off, when you reach that let-off point, it would only require about 14 pounds of pull to complete and hold the draw instead of the 70 pounds it took to get to the let-off point. So the advantage of holding just 14 pounds while completing the aiming process instead of trying to hold 70 pounds is a real game changer.
Recurve Bow with Descriptions
Draw weight is one of the most contentious aspects of bow selection, and it is something about which a great deal of misinformation abounds. It is generally assumed that a higher draw weight will lead to a faster arrow speed, and therefore to a flatter trajectory. A flatter trajectory means that you don't have to compensate for distance to the same extent, which makes a faster arrow particularly important in field archery, where the distances will vary throughout the course. In addition, a faster flight gives the arrow less time to be affected by wind.
This assumption -- that a heavier draw will lead to a faster flight and a flatter trajectory -- has a flaw: it does not hold up. It is incorrect for two reasons. First, if you use a heavier draw, you need a stiffer arrow. If you shoot an arrow designed for a 20 lb draw from a 50 lb bow, it will not hit the target consistently, even assuming it doesn't break. Stiffer arrows are thicker, and therefore heavier, than less stiff ones, and therefore fly more slowly for a given draw. If you do the mathematics, it turns out that, increasing draw weight leads to a slightly faster arrow, the difference between arrow speed for a 35 lb bow and a 55 lb bow is negligible for all practical purposes. As a weapon the heavier draw is vital because, even though the arrow will not be travelling much faster than one from a lighter bow, the increased weight of the arrow will impart a greater amount of energy to the target, and therefore do more damage. For any kind of target archery, however, this consideration is irrelevant.
The second reason why a heavier draw can actually be a disadvantage is that it is much harder to maintain a steady aim while pulling back a string at your full muscular strength. Even if you can pull a 55 lb bow, you're never going to be able to hold it as steady as a 35 lb bow.
For recurve archery there is an optimal draw weight for any person, and exceeding that draw weight will not offer any advantages. For most men the optimum is in the 30-40 lb range; for women it is 25-35 lb. No beginner should ever be required to draw a bow with a weight more than about 15 lb, even if he or she can do so without too much difficulty. Again it comes down to getting the basics down before advancing to a heavier draw weight.
With a compound bow the situation is a little more complex. Since draw weight decreases as you come to full draw, you can decide either to have the same peak draw as a recurve, but with easier sighting (because you'll only be holding half the weight when you're sighting), or you can accept the same weight at full draw and have twice the peak draw. For example, if you can sight comfortably while drawing 35 lbs, you could pull a compound bow with 60-70 lb peak draw. But, as described above, you probably would not do so, because there are no advantages for target archery. If you choose a compound with a 45 lb peak draw, and assuming a 75% let-off, you will be holding about 11.25 lb at full draw -- which is trivial -- and your arrows will travel just as fast as those shot by a 60 lb bow because they will be much lighter.
As you can easily see, determining the proper bow weight is a complex issue. Suffice it to say, your ideal draw weight will be the weight you can comfortably draw to full draw and hold through the aiming process. For a compound bow the proper draw weight is what peak draw weight can you manage with good form while getting to full draw.