MRI reconstruction using windowing based apodization
You say:


I have a 128 point one dimensional k-space samples...
The hanning window is the same size as the k-space vector (256)...


Make sure that you have the appropriate sizes in your algorithm.


Next, I convolved the k-space signal with the hanning window...


Windowing is applied in $k$-space by multiplication - you simply have to multiply your window and the original $k$-space line. In image space, this is a convolution, hence you could take the Fourier Transform of the window function and convolve the image with it. 

Another view: 
Apodization is applied to suppresses certain frequencies. For example, the highest frequencies are simply skipped by setting them to 0 due to the multiplication of the window function and the $k$-space data. If you were to convolve the two, you would "spill" the information of the higher frequencies all over $k$-space - which certainly is not what you want to achieve by apodization.