How to use weight variables within aggregated results, for group proportions If I have the following data, where each row represents and individual
response, how would I go about reporting the proportions of different groups?
(here the groups are paper, door, and not sure)
Columns:

*

*question_response - the response to the survey question "do you prefer doors or paper"

*weighting_variable - a weighting adjustment, an adjustment weight to each survey respondent

Rows :

*

*individual responses

   question_response  weighting_variable
0               door                0.51
1               door                0.49
2               door                1.05
3               door                1.36
4               door                2.24
5               door                0.34
6               door                0.75
7               door                1.95
8               door                3.26
9               door                0.52
10              door                1.99
11          not sure                0.38
12             paper                0.94
13             paper                0.41
14             paper                1.29
15             paper                0.18
16             paper                1.03
17             paper                0.58
18             paper                0.07
19             paper                0.65

Just looking at the group counts, before considering the weights there are:

*

*40% prefer paper

*5% are not sure

*55% prefer doors

My question is how to consider the weights, my intuition is that they should
be considered as follows.
First for door, the average weight is
0.51 + 0.49 + 1.05 + 1.36 + 2.24 + 0.34 + 0.75 + 1.95 + 3.26 + 0.52 + 1.99 = 14.46

14.46 / 11 = 1.314545

Then paper is 0.643750, and not sure is just 0.380000
Based on this I would instead say that

*

*40% * 0.643750 = 25.7% prefer paper

*5% * 0.38 = 1.9% are not sure

*55% * 1.31 = 72.3% prefer doors

This makes sense as the percentages are still summing to 100 (within some rounding), but I wanted to double check that this was correct .
 A: More details on the actual problem could be of help in arriving at perhaps a more meaningful solution as to "how to employ weight variables within aggregated results, for group proportions".
For example, assume your data represents a buyer's product preference (product here I would presume to be the 'door', 'paper' , and if no preference,'not sure').
The weight represents the certainty of the responder's answer based on a survey scale (say 1 to 5).
What one could do with this data is, for example, assume that the scale translates into a probability 'p', whereupon with repeated occurrences of the buying decision, the sales selection could go to another item.
In this context, I would recommend a Monte Carlo simulation approach where the sales selections are probabilistic observed and proportions recorded over a large number of iterations.
This results in an average product selection proportion for each product,  a confidence interval from repeated runs, and even a possible plot of the observed probability selection distribution around the observed product averages.
Also, one could assess the sensitivity of the results as to how the buyer's preference scale is translated into probabilities. There is also a question as to how accurate a responder's hypothetical answer is compared to actual buying behavior, all of which could be transparently addressed in a simulation approach.
