My answer is YES. (all of the above)

If you want large fruit then you need to thin them to about 1 fruit every 4 to 6 inches.

If that still weighs the limbs down then thin them more or support them with props or

tie them to a stake which you do not have.

If you do not it WILL break the limbs off of the tree.

I can't see the picture well but it looks like you have 100s of fruit and should start with thinning.

I see now that I can click on the picture and get a slightly larger view.

Yes, please thin them aggressively. I know that it hurts but I would leave less than half of them.

Definitely thin and thin more toward the ends of the branches to keep more of the weight towards the stringer end of the branch. A rule of thumb is to keep a palms width apart between the fruit. You can modify this to thin heavier towards the end of the branch and lighter toward the trunk.

Prune your trees and you won't this problem next year.