Canning question - does the jar need to be full?

You need to leave about 1/4 inch headspace for strawberry jam regardless of whether you are processing quarter-pints, half-pints, or pints, all of which process for 5 minutes at sea level, 10 minutes from 1,000 to 6,000 feet altitude, and 15 at altitudes above that. (Also keep in mind that you need to sterilize jars and bands used to preserve foods processed less than 10 minutes at sea level--always use new lids simmered in hot water to soften the rubberized flange.) SKK is correct: the tables for processing times are calculated based on the time it takes to press the air out of the food, including the empty space in the jar. If you leave more than the proscribed amount of headroom in a jar then the processing time may not be adequate to create a vacuum, your seals will fail, and your product will not be shelf stable.

Skk is correct...but don't give up hope! You can freeze the jam. Ball jar makes an 8oz plastic jar that is perfect for freezing jam. Enjoy!

If too much headspace is allowed, the food at the top is likely to discolor. Also, the jar may not seal properly because there will not be enough processing time to drive all the air out of the jar.
Source: http://www.uga.edu/nchfp/questions/FAQ_canning.html#4