Steady weight gain isn't an issue. I'm an omnivore and I can go three weeks at one weight and then all of a sudden be up three pounds (for good, not just water weight) on week 4 or 5. To my knowledge, that isn't necessarily indicative of anything good or bad.
Like lilmamita said, there's no such thing as having to combine certain foods at a meal to make a complete protein. The key is variety. Your RDA of protein as a pregnant/lactating mom is going to be 70 (ish) grams per day. If you don't eat eggs, you'll have to make a more concerted effort to get enough protein, IMO. Per HappyCow.net (a veg resource guide), here are some of the following good sources of vegan protein:
Protein in Legume: Garbanzo beans, kidney beans, lentils, lima beans, navy beans, soybeans, split peas
Protein in Grain: Barley, brown rice protein, buckwheat, millet, oatmeal, quinoa, rye, wheat germ, wheat, wild rice
Vegetable Protein: Artichokes, beets, broccoli, brussels sprouts, cabbage, cauliflower, cucumbers, eggplant, green peas, green pepper, kale, lettuce, mushroom, mustard green, onions, potatoes, spinach, tomatoes, turnip greens, watercress, yams, zucchini
Protein in Fruit: Apple, banana, cantaloupe, grape, grapefruit, honeydew melon, orange, papaya, peach, pear, pineapple, strawberry, tangerine, watermelon
Protein in Nuts and Seeds: Almonds, cashews, filberts, hemp seeds, peanuts, pumpkin seeds, sesame seeds, sunflower seeds, walnuts (black)
What do you normally put on your protein-bread sandwich or bagel when you have it for breakfast and/or dinner? By having a nut butter on it or oodles of veggies, you're probably right around where you should be for your daily protein level. Nut butters and whole grains should be your BFF right now!
It's been my experience that anemia can sometimes be tied to low B12 levels as well, so since you're not eating eggs or meat, I would make sure you're taking additional B12 with your care provider's blessing. Despite taking Floradix and blackstrap molasses/OTC iron supplements, on my two vegetarian/vegan pregnancies, I was borderline anemic (10.4 down from a 12.3 starting level). We later determined that it was low B12 levels that were sandbagging my hemoglobin counts. 6 months of continued postpartum supplementation with B12 (pills, not shots) and iron turned things right around for me. Also, calcium-containing foods inhibit your absorption of iron, so if you're only borderline on getting enough iron, you may want to watch your cheese intake, or space it further away from your supplements or the times when you eat iron-rich foods.
As far as what happens with a low birthweight (LBW) baby, it depends on just how low the birthweight is and what exactly your doctor was trying to imply by stating this. If you deliver at full term and your baby is over 6 pounds, he/she will just be a small baby and will likely catch up. But if you're looking at intrauterine growth restriction (IUGR) or small for gestational age (SGA) then it may get more serious both in terms of what happens post-delivery at the hospital and what that may mean health-wise for your baby. SGA babies usually catch up by age 2 without any lasting effects, but IUGR babies are at increased risk for stillbirth and neurological development issues. That being said, I am sure/hoping that your doctor was just trying a sort of "scare" tactic to encourage you to watch your iron and protein now and if you were truly at risk for either IUGR or SGA that he'd be more forceful in his recommendations.