Here are detailed explanation of how each operators works:

To Start: have a mesh ready and bind it to an armature. Select a Single mesh object and enter edit mode.

1. Vertex Weight Toggle: this acts like a master switch to determine if any of the operators would run, at the same time, it turns on some viewport shading.

2. Increment and Increment Macro sliders: these determine how much weight should add/remove when using Add Weight, Add Micro Weight, Reduce Weight, Reduce Micro Weight (both fill and gradient)

3. Add Weight, Add Micro Weight, Reduce Weight, Reduce Micro Weight (both fill and gradient): after you have select more than 1 vertices, use shortcut to adjust their weight value. for example, I have selected 3 vertices from vertex group A, vert1 has 0.1 weight, vert2 has 0.2 weight, vert3 has 0.3 weight. Fill method will first sample the first vert in the order and use its weight as start point, uniformly adjust the value, such as all of their value will increase from 0.1 to 0.2 to 0.3 etc. Gradient method will adjust them individually, such as vert1 from 0.1 to 0.2 to 0.3 while vert2 from 0.2 to 0.3 to 0.4 etc.

by default, Shift + Scroll use fill method, Ctrl + Shift + Scroll use gradient method. you can change hotkeys and enable/disable operators in addon preference.

4. Copy Weight: this will copy all weight value as last selected vertex. take the previous example of 3 vertices. if I select vert1 then vert2 and lastly vert3, use copy weight will make all their weight value to 0.3. if I select vert3 and vert2 and lastly vert1, use copy weight will make all of their weight to 0.1

5. Smooth Weight: this will smooth the selected vertices weight value with regarding to their adjacent vertices. in the first pass, I usually select a large portion of mesh, use Add Weight (Fill) and Select Boundary Loop then use Smooth Weight to ease the weight transition.

6. Switch VG: when adjust the vertex weight, it work on active vertex group. for example, a single vertex may have weight 0.1 with vertex group A, but weight 0.5 with vertex group B, Switch VG provide a easier way to pick which vertex group to be active rather than going through the vertex group list and click it. With nothing selected or more than 1 vertex selected, you can move mouse cursor near a bone and use shortcut to run the operator. it will switch to the vertex group under the mouse cursor.

if a single vertex is selected, it will cycle all its influenced vertex groups

7. Auto Normalize Toggle: when it is on, any weight adjustment will make sure the total value is 1. for example, vert1 has influence in 3 vertex groups A B and C. weight 0 in group A, weight 0.5 in group B and 1 in group C. when group A is active and Auto Normalize Toggle is on. every increment of 0.1 in group A, group B and group C will decrease but maintain a 1:2 ratio until weight value get to 1 in group A, group B and group C goes down to 0.

8. Select Half Vertices: it will select half of the vertices along x positive direction, if Invert toggle is on, it will select the x negative direction.

9. Mirror Weight: it will transfer weight value to selected vertices from relevant mirror parts. for example, I have rigged a human character and done a simple binding. I adjust the weights on left forearm and left leg. then I select all right side vertices and press mirror weight. right forearm and right leg would have similar mirrored weight.

10. Vertex Group Limit: it will remove vertex group from the smallest influence and only keep total vertex groups based on a set number. take the previous example of vert1 in groupA(0), groupB(0.5) and groupC(1), if set number is 3, nothing will change. if set number is 2, the smallest 0 from group A will be removed. if set number is 1, group A and group B will be removed.

11. Check Exceeded Groups: it will select any vertices that have more than the set number of vertex groups. for example, if the set number is 3, any vertices that have more than 3 vertex groups will be selected. 

12. Remove Weight: on selected vertices, it will check every single one's vertex groups. if the vertex group's weight value is below the set amount, it will remove the vertex group. take previous example of vert1 in group A (0), group B(0.5) and group C(1). if set number is 0.6, group A and group B will be removed.

13. Check Weight Sum: each vertex may have multiple vertex group and each has different weight value, this operator will select any vertex that have total weight below or above 1. the previous example if vert1 in groupA B and C will be selected, since the total value is 1.5 (0+0.5+1).

14. Normalize Weight: this will auto adjust the weight value based on the ratio and make sure total equal to 1. 

15. Active Vertex Weight Groups: when a single vertex is selected, it will show its vertex groups value, it may offer assistance of the set number of Remove Weight.

16. Scrub Timeline: when Vertex Weight Toggle is on, you can scrub the timeline by holding "J" key and move mouse left and right. Generally, when I adjust skin weight, the character bones has some animation data, scrubbing the timeline, it is easier to spot the problem area and make finer adjustment. 

there are two area for scrub timeline, all in 3d viewport. Scrubbing in orange area is straight forward. the speed can be adjusted with Scrub Multiplier in MISC tab. Scrubbing in red area is corresponding to the whole timeline, regardless how many frames there are, scrub to the right will always reach the end frame.

If it is not already, Enable the on cage and edit mode toggle from armature modifier

if you want to change the hotkey "J", here is how: find the addon folder, C:\Users\UserName\AppData\Roaming\Blender Foundation\Blender\3.6\scripts\addons\Handy Weight Edit, open "__init__.py" with text editor and search keyword "change". in these two places replace "J" with another CAP letter, such as "K". save the file that is it.

17 Isolate Active Bone. while adjusting different vertex groups, use the toggle to only show the corresponding bone, so that you would never modify the wrong bone influence. for complex rig with hundreds of bones close to each other, make only the relevant bone visible together with the bone name shown, greatly reduce the possibility to modify the wrong one.

in blender 3.x, armature use bone layers to organize the visibility. toggle the deforming bone layer on in Armature -> Data -> Skeleton -> Layers. if you use rigify, it is layer29, whereas with auto rig pro, it is layer 31.