That is exactly what the nlfilter() functions does. Here's your demo:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
imtool close all; % Close all imtool figures if you have the Image Processing Toolbox.
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
A = imread('cameraman.tif');
[rows columns] = size(A);
A = im2double(A);
fun = @(x) median(x(:));
B = nlfilter(A,[5 5],fun);
subplot(2,2,1);
imshow(A)
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Give a name to the title bar.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off')
% Display image B
subplot(2,2,2);
imshow(B)
title('Function applied to image', 'FontSize', fontSize);
% Get array of weights the same size as the image.
weights = peaks(256);
weights = weights - min(weights(:)); % Make all positive.
subplot(2,2,3);
imshow(weights, [])
title('Our weights', 'FontSize', fontSize);
% Multiply weights by image.
outputImage = weights .* B;
% Display image outputImage
subplot(2,2,4);
imshow(outputImage, [])
title('Now with weights applied', 'FontSize', fontSize);
