I don't think
estimating is the correct approach to climbing trees.
See, from mechanics, the tree branch is a cantilever beam. So comparing branches could be done if stepping only at the base of it, only with one foot.
Then there is the variable is the branch live or dried out.
Lastly, calculating the strength of a branch would include not only successfully identifying the type of tree, but will also be very sensitive to the diameter of the branch. Are you going to be carrying sub-mm accuracy callipers and measure each branch?
Having said that, my approach to climbing trees is as follows:
Follow the 3-point principle. At any moment of time, have three points of stable attachment to the tree. If you slip or a branch breaks, you should NOT fall, but hang on the remaining two.
Look out for dry branches. Be very sceptical towards their strength.
If in doubt, test the branch. With a leg or hand, push the branch downward about half a meter from the base. Get a feel for how much it bends. If it looks safe, step at it's base, right next to the three trunk.
Look back often. It is no fun to discover that you have reached your goal ... and now can't climb down safely.