What would the pH change be if I drop one gram of sodium hydroxide into a pH 8.1 solution
If we know that the pH is 13 (let's take it as 13 for the simplicity), then we can back-calculate the concentration of sodium hydroxide in this solution from $\ce{14=pH + pOH}$. This gives us pOH=1, thus the concentration of sodium hydroxide of 0.1M. Since 0.1M sodium hydroxide is hardly a very concentrated solution, we can safely assume that 1 gram of the solution is going to be roughly 1 mL. Thus, with each 1 gram of the lab solution you're adding about 0.0001 moles of $\ce{NaOH}$ into your 1 liter of sea water giving you $1*10^{-4}$M solution with the pH = 10. 

Using the same trick to calculate the concentration of $\ce{OH-}$ in your sea water as we did for the stock sodium hydroxide solution, we get about $1.25*10^{-6}$M, which is negligibly small compared to $1*10^{-4}$M solution that you get after adding sodium hydroxide to it. Thus, after 1 gram of sodium hydroxide in a liter of sea water your pH should go from 8.1 to about 10. If you add 2 grams, you'll get a $2*10^{-4}$M solution, which yields pH of about 10.3.