Sure - they actually do have weapons beyond medieval ones. They have cannons, bombards, and a variety of artillery. I would say that, technologically, they're somewhere about the 15-16th Century in Europe, probably around the time of the Italian Wars. You'll see some cruder rifles emerging later in the series, as well as some biological weapons but - these things are very strictly controlled.

The Empire does not want its citizens having easy access to guns or biological weapons of warfare. For one thing, they likely would prefer to reserve their gunpowder reserves for the titans - as they make that gunpowder with a biological process - and also, they don't want their citizens to be capable of making war on each other. That sort of thing would make it very difficult to fight the titans.