I parented the rig using Empty Groups then weight painted a section. The vertex group seems to not act according to the weight paint and the points all have a weight value of 1.
If you parent With Empty Groups, by default the vertices won't be assigned to any vertex group, you need to assign them in Weight Paint mode or with the Assign button.
If you assign a vertex to only one vertex group, even if the weight is very low (like 0.001), the influence of the bone on it will be 100%. So what you need to do is begin to assign the vertices to the other vertex groups, if a vertex is assigned to another vertex group, its weight will be taken into account.
For example if a vertex is part of 2 vertex groups with a weight of 0.001 in both cases, the influence will be shared 50/50 between the 2 bones. If it is part of a vertex group with a weight of 0.1 and of another one with a weight of 1, the second bone will be ten times more influential, etc.
But what you could have done in your case is parenting With Automatic Weights. There's an error message because you have overlapping vertices and very dense topology. To fix that select all in Edit mode and press M > Merge by Distance. Also unparent the object (AltP), shift select the armature, scale both the object and the armature like ten times (S10), it makes the calculation easier in the case of dense topology, parent With Automatic Weights, then scale down to the original size (S0.1).
To give some corrections afterwards, select the armature in Object mode, shift select the object, switch it to Weight Paint mode, select the desired bone and paint.