Fundamental misunderstanding of windowing
Your description of windowing a 2D image filter kernel, fits into a discrete-time FIR filter design method. Hence I will assume you are mixing windowing as a filter design method vs windowing applied to signals for Short-Time Fourier analysis or windowing applied for block-based processing of long signals. So please make it clear which action you are performing and the context of your intentions.

Then let me briefly describe windowing as a filter design tool.

An ideal discrete-time frequency selective LTI filter will have an infinite length and noncausal impulse response $h_i[n]$. So it shall be truncated and delayed for any practical FIR convolution applications.

Given an ideal filter impulse response $h_i[n]$, you obtain the coefficients of the practical impulse response $h[n]$ of length N samples via

$$h[n] = w[n] h_i[n]$$

Which is the point wise multiplication of the filter $h_i[n]$ with a window sequence $w[n]$ of length N. The main purposes of the window is to first truncate the infinite length ideal impulse response, and then to try to cure the side effects on the resulting filter spectrum caused by the crude truncation.

There are many different types of windows such as box-car,triangular, Hamming, Hanning, Blackman, Kaiser. The box-car is the crude rectangular window without any tapering. Other windows perform varying degrees of tapering at the ends of the impulse response so as to achieve a tradeoff between filter transition bandwith and passpand / stopband peak ripples. 

Note that the windows's frequency response $W(e^{j\omega})$ is convolved with the ideal filter frequency response $H_i(e^{j\omega})$ which yields the frequency response of the practical filter;i.e,

$$H(e^{j\omega}) = \frac{1}{2\pi} H_i(e^{j\omega}) \star W(e^{j\omega}) $$.