Yup (to what SLM says),
Couple more thoughts/comments.
If you were to do your chimney as shown, but in 1/8th bass legs, with 1/16th balsa bracing (if you're buying wood from a hobby store, try to pick heavier/stiffer ones), you would save a lot of weight. Built with any reasonable level of precision, it will hold 15 kg- actually should hold significantly more, but trying to get you quickly to something a lot better than what you have now.
That same combination will be more than enough in the base. Look at the pictures of C-Div bases in the Gallery to better understand how simple it can/should be, compared to what you have now. 4 legs, 4 "ladders" joining the tops- the tops of the base legs line up with the bottoms of the 4 chimney legs. 4 ladders joining the mid-points of the base legs. X- braces (using the 1/16th balsa), joining the upper ladders and leg mid-point ladders, and from the leg mid-point ladders down to the bottoms of the base legs. You probably won't need it, but for a safety factor, with minimal weight, run a "strap" around the bottom of the base, using 1/16th balsa.
Consider using slow CA glue - it will save you a lot of waiting for glue to dry time. For the problem of joints not fitting/filling, and filling with glue, sand, or use a little file to get a good fit.
Make sure the bottom ends of your base legs are sanded/filed so they are flat and in full contact with the...ground. Then make sure the tops are flat, and provide a LEVEL base for the chimney to sit on. Before putting chimney on the base, make sure the bottoms of the chimney legs are sanded/filed so it sits straight up and down. This is really important- lean will kill you
Fort Collins, CO