ATI 6770 1GB vs 2GB in HP dv7t laptop

[Steve]

I have an HP dv7t laptop with a 1GB ATI 6770 video card in it. I need to
play 1080p HD video on screen 2 and have it NEVER
hiccup/pause/blink/whatever, and have it do it all day long. I have found
on rare occasion 1080p video will pause for 1/4 second or so. Not good.

Will getting the same machine with a 2GB 6770 help this? Or is the
bottleneck somewhere else? BTW my HP also has a 7200rpm hard drive and 8GB
RAM.

Thanks,
Steve