The font itself isn't thicker.

Here's what I did to make that image:

I took yours, used the rectangle selection tool to select "THE WHOLE BLOODY AFFAIR," cut it out of that layer, pasted it onto a new one, then used Edit>Transform>Scale to change the size. You can stretch it to be taller or shorter, wider or slimmer that way.

What I'd do is take a screencap of the "KILL BILL" from the DVD (without the "Vol. 1") at full 720x480 size (saved as a TIFF or PNG, and not as a JPG), bring it into Photoshop, add the new text (the process I described above can be done to a text layer as well, not just an image layer), put it where you want it, flatten the image, save it, then import it back into your video editing program and match it up to the real logo, adding fade-in/fade-out as necessary to get it to match.