[1]  Our starting point is this marble sample.

[2]  A test with the offset filter at 50/50 shows the tonal value is a bit off, being darker on the right. Undo the offset and apply a graduated black to white paint-on or new layer mask

[3]  Use the levels adjustment to lighten the right hand side. The mask can be inverted and adjustments made to the other side if necessary. Check your adjustments using the offset filter and the undo.

[4]  When happy that you have an even tone the image can be finally offset 50/50 for real. This will, of course, result in a mismatch across the central axis.

[5] To blend these edges I used the Clone Brush, set to a size which sort of matches the image texture, 6 pixels wide in this case. You will need to reset the brush several times, taking samples from anywhere in the image that will blend over the seam. Try to follow the 'look and feel' of the existing texture. View the image at actual size and 200% alternately as you work.

[6] When you're happy that the join has been blended satisfactorily, test it by tiling the image, paying particular attention to any distinctive shapes which might be creating a patterning effect.

[7] In this case, there's a larger dark area at the centre/top which stands out. This is cured by breaking the area up with orange texture, again using the Clone Brush.

[8] The final result. A full size version of this is in the free textures section