Load ratings are not determined by any standard method from one company to the next. As a way of estimating load ratings I used to recommend that people go to the abandoned website of the old Bell Canoe Works and look for a canoe of roughly the same dimensions as the one in question, and look at the loads required to sink the boat to the depths indicated (I think they ranged from 2 to 4 or 5 inches). Alas, that old website finally got taken down. The next best thing would be to go to the website of the new Northstar Canoes and do the same thing, as I’m pretty sure they use the same system. The only trouble is that they have far fewer canoes, and thus far less variety in canoe dimensions for comparison.
You haven’t said how long the boat is or how wide, but it’s pretty typical for 16-foot canoes to have a reasonable rated capacity somewhere in the range of 600 pounds (that’s VERY approximate). For any 15-footer that’s not as wide as a barge, 500 pounds is likely a reasonable limit. Certain manufacturers rate their 17-foot canoes at right around half a ton, but that’s not realistic in most cases. I think for boats having such a rating, that’s the weight that sinks the canoe to the point that there’s 6 inches of freeboard. That isn’t much, and more than that, the canoe will handle like a pig due to how much hull is below the surface. You are better off assuming that 5 inches of draft means you have a very heavily loaded boat. 4 inches is more practical as an upper limit, and 3 is usually better yet (again, check out Northstar’s website for some approximations). Sometimes in strong wind, more draft (more load) is better, but on average, you will pay for extra load in paddling effort. For one adult and two or three kids (of unspecified age and size, so far), you are better off keeping your load on the light side, since their combined weight may be significant, yet you probably will be supplying more than your share of the paddling power.
Next, you should do something about those paddles. Using them will be as bad or worse than having on overloaded boat. For starters, go to the Bending Branches website. They have quite a range of decent paddles for prices that are as low as anyone’s (though the prices may be higher than you expect), and I’m pretty sure they have sizing recommendations, and that also can be modified according to how high the seats are, etc, but usually the standard recommendations are good enough, especially starting out. Sawyer paddles are similar in quality, for similar prices. You can order both online at Rutabag.com, among other places, and probably direct from the manufacturers. For myself, I find that paddles in the “pretty good” range of quality can be gotten for around $230, plus or minus. Bending Branches might still have some decent, practical choices for about $150. For what it’s worth, one of my favorite Bending Branches models is the “Expedition Plus”. It’s incredibly tough, and moderate in weight.