There are a number of designs on the net that I found with a simple search. Google image search produces images from the merely functional ones like the instructions linked here through to quite realistic looking ones that appear likely to work.
or this big one
The key for a simple, easy to build one is to use wheels on the base. It will shake back and forth when fired which means the structure does not need to be as strong. If you don't do that then the base will need to be similar in size to the arm, as in both pictures above. I am a little surprised that there's so little bracing on the arms of these models, as you can make a much stronger model using a tension member at least on the top of the arm, if not below.
But with Lego the main issue will be the density of the weight. Lego doesn't do high density part, so most people use non-Lego weights. Since you're willing to do that it's easy - the first picture shown has a lead weight, which is why it's hard to see that there's a weight at all.