This section is used to modify the node's final output value.  It is only useful for designing fuzzy logic systems, or a fuzzy logic section of a system.
Please note:   The Weight controls only modify the individual instance of the selected node(s) on a Logic Board.   Thus, the Weight controls are only visible when a node is selected on the Logic Board.  The controls are not available when a solver is selected in the Solvers panel, because the original solver's output can not be globally modified.
This behavior is different than BloodHound 1.0.  In BH 1.0, the Weight controls modified the nodes output globally (every instance).  This change in BH 2.0 adds more system design granularity.

Multiply Output:   This takes the internal values (the Long and Short values determined via the Properties tab » Output Rules section) and multiplies them by this value.  Note: the final output will not exceed a value of 1, as described in the Slider control below.

Slider control:  The slider constrains the final output to a value of 0 to 1.  The left side of the slider sets a minimum value that is output regardless if the solver condition is true or not.  The right side sets a maximum value that is output.  The output is capped.
e.g.  Three indicator conditions are being checked, and thus three solvers are created.  Only two out of the three indicator conditions are needed.  An Additive logic node is used to add the solver's outputs together.  Just two out of the three solvers need to add up to a value of 1.  Therefore, the right slider (max output value) for all three solvers is set to 0.5.  When two indicator/solver conditions are found, thus the outputs = 0.5, then the calculation, in the Additive node, is 0.5 + 0.5 + 0 = 1.  A value of 1 means the two out of three condition is true.

Hedge Operation: This applies a mathematical formula to the internal value.

None:  No modification is applied.
Very (square output):  A squaring formula is applied.  Output  =  value^² .
Somewhat (square root output):  A square root formula is applied.  Output  =  √value .