Interactive example - why my implemented network doesn't use weights

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I want to make this simple & intuitive. You'll get the chance to draw a node on my image using weights.

Little background info, please read it a bit:
See image 1 below. My code generates that image. My input nodes (leafs) are A-Z. It builds bigger and bigger text sequences the higher you go up. Massive net. It models descriptions of the world aka knowledge. But there's no weights. Every non-leaf node is made up of 2 lower nodes. The parent node 'is' its 2 children nodes. Hell+o = hello. Only the nodes that completely contribute bother to connect (all or nothing fires), for example "hello" is not made of node "z" and hence not connected. z could weigh in on "hello" as 11% contributing and be neglected to 0% but then there's no need to, it's either fire, or not fire. Hence "z" node doesn't even bother connecting to "hello" or "he".

See image 2. Can you draw on this mostly blank image the node representation "hi" using the alphabet letters drawn? Please draw the lines, circle, and weights. It's just 1 node to add, very small simple text net.