While that's not a lot of weight, it is more important for your weight gain to come in later pregnancy that in early pregnancy (it's also easier to lose if you gain it later than earlier). Increase your fat and protein intake...what's finishing developing now is the brain and nervous system, plus the fat stores in your baby, so you need those two things. Eat avacado, olives, nuts, fish, as all have good fats and protein that your body can use...also eat whole grains like brown rice, stone ground whole wheat breads and pastas, oatmeal, etc.
As for the preterm delivery...one person's history doesn't make it yours.
My grandmother never carried a baby to term--all were born prior to 37 weeks. My mother carried me to term and my brother past (I was 40w0d and my brother was 40w3d)...I however, have not carried a baby to term, BUT, both of my babies were perfectly healthy and no NICU stay (even the one born at 34w0d).
Just eat healthy, make certain your calcium, fat and protein levels are high enough (you should be eating no less than 2000 calories per day, and if you have a high metabolism more like 2200) and just go with it. I only gained 12lbs total with my first (but that was only to 34 weeks) and 9 with my second (37w3d)...I was average/low weight for height when I got pregnant with my first and about 20lbs overweight when I got pregnant with my second though.