This is not as simple as it seems...
To work out how much weight each branch may hold, you will need to do the following..
Remove all the apples from one branch, and weigh them together, divide by the number of apples you have, to get your average apple weight.
Measure the length of this branch.
Now attach a spring balance to the end of it, and pull down until the branch breaks, making a note of the spring balance reading at the exact moment the branch broke.
Let us now assume your branch was 2 feet long, and the diameter of the branch was 1/2" where it broke, and it required 10 lbs of force to break it.
As the branch broke at 2 feet with 10 lbs force, it would need 20 lbs force at 1 foot to break. Work out the cross sectional area for 1/2" dia, which will be 0.1964 square inches.
Divide 1 by 0.1964 to give approx 5, multiply this by 20 lbs, which gives a breaking load of 100 ft lbs per square inch.
For each branch measure the diameter where you think it would break, and work out the cross sectional area. Measure the distance to each apple on this branch, in feet. Now multiply that distance in feet by your average apple weight in lbs, do this for each apple on that branch, and add them together. This will give you the total foot lbs torque on this branch.
Divide 1 by the cross sectional area of this branch and multiply by the foot lbs figure you have, provided the answer is less than the 100 ft lbs figure, the branch will not break.
I would allow a safety factor of 2, to allow for wind and rain, and them pesky birds.
So now you will need to work backwards, removing apples to the point where the total torque does not exceed 50 ft lbs.
Just substitute your own figures for the ones above, and you are done.........