I'm going to try to be as careful as possible in answering this, since I'll easily confuse myself.
Specific gravity is a measure of density. It compares the density of whatever you're measuring to water. So distilled water would have an SG of 1.000.
Increasing salinity does increase density, trouble is, it's not 1 to 1. For example, the average salinity of seawater is 35, but this only changes the density to 1025kg/m^3, or an SG of 1.025.
You can play around with the UNESCO Equation of State, although it's probably messier than most aquarists would like to get into.
This may help. Dan Kelley has an EoS calculator:
http://www.phys.ocean.dal.ca/~kelley/seawater/density.html
You can figure out the salinity you want, and then you're set. The salinity that you get is in parts per thousand (PPT) which translates to grams per litre. I'll leave the litre to gallon conversion to you if you so desire, but I'm guessing it's about 4g/gallon per g/L.
This should allow you to dose smaller batches from bulk salt. To get to more conenient units (like cups/tbs, etc) you just need the g/cc density of your sea salt.