Will I still have a safe delivery if I look really big?

You should. Being "big" should not necessarily cause any issues with your pregnancy unless you have specific conditions such as gestational diabetes or are a diabetic and your baby is very large. This would/should be known and followed by your dr. And preparations could be made for a safer delivery.
Yes. Everyone carries differently. Looks can be deceiving. Your doctor should measure the size of your uterus every visit after 20 weeks. This is a quick way to check the size of the baby. If your measurement is too much then your doctor may get an ultrasound. Keep in mind though that ultrasounds are not that accurate at predicting the weight of the baby.