What would cause blood pressure to be relatively normal in the morning, but then gradually increase?

Several things: Probably the most common cause is that people who take meds to lower their BP and take them in the morning have their meds wear off during the day. Another cause is eating salty food for breakfast or lunch (salt on your eggs? Bacon?). Activity, stress, and fatigue can raise BP later in the day. You are likely most relaxed shortly after getting up. There is a normal diurnal variation in BP as well.