I don't think there is any way to find the weight if the label is missing. The only thing you could tell is whether it's fine, medium, or thick.

Your best bet would be to do a swatch and measure how many stitches and rows it takes to make an inch. Armed with that info you can then look at other labels to see if your swatch matches. Since this is a swatch for guage, you can also go through patterns and check the guage called for.

Actually, although I still it's pretty much a "guestimate", there is a way to determine this. Check out this site:

Here is a link that might be useful: wraps per inch

Thank you both for replying.
Appreciate the answers.

I also participate on the Ravelry site and they also have a similar chart to the link Donna posted - I copied/pasted some of their information here:
Ravelry Standard Yarn Weights
Wraps per inch/Gauge
Fingering - 4 ply - 14 wpi/28 stitches = 1 : Super Fine
Sport - 5 ply - 12 wpi/24-26 stitches = 2 : Fine
DK - 8 ply - 11 wpi/22 stitches = 3 : Light
Worsted - 10 ply - 9 wpi/20 stitches = 4 : Medium
Aran - 10 ply - 8 wpi/18 stitches = 4 : Medium
Bulky - 12 ply - 7 wpi/14-15 stitches = 5 : Bulky
Super Bulky - 5-6 wpi/8-12 stitches = 6 : Super Bulky