Is it okay to continue breastfeeding throughout my pregnancy, or do I have to wean?

No. It is probably best to refrain from breastfeeding by 18-20 weeks due to risk of preterm labor from the breatfeeding hormone reflex initiated. In addition, the fetus will require a well supported nutritional enviorment which may be compromised by the excessive caloric demands of the child as well.
Yes. Typically it is safe to continue nursing while pregnant. There may be a decrease in the quantity or quality of your breastmilk at some point. You should also make sure you continue your vitamins and a well-balanced diet. If at any point it becomes too fatiguing to nurse while pregnant you should listen to your body and consider weaning. Ask your doctor or lactation consultant for advice too.