There is more than one possibilty here. You have not told us how you control your bgl i.e. what meds you are on, what diet etc, so I will have to generalise here.
Firstly, it could be due to eating high protein or fat late in the evening, or a bedtime snack. I found that the timing of my evening meds was important, and if I take them too early, then they lose eficiency over time, so I have to drop my meal into the middle of that window. i found that I need to take my metformin half an hour before the meal so that it has disolved in time to block the glucose absorption in the gut. Once glucose has entered the bloodstream, then Metformin has very little effect. It also loses effectiveness with time, so will be less useful if the meal is delayed too much. Fat and protein take longer to convert to glucose than normal carbs, which is why I say a late meal with high fat and protein is not a good idea. I delay my Gliclazide tabs till my 2 hr PP reading, since it stimulates insulin, and works on glucose already in the blood. This timing allows me to adjust the dose depending on how my bgl is reacting to the meal.
The last question I need to ask is - do you test bgl late at night, so is the morning reading higher than the bedtime reading, or is it just a hangover from the night before. If it is not lower than the post meal reading, then it may be the medication needs changing in either dose or timing as already discussed above.
Second thing to consider is what is called Dawn Phenomenon, which in itself has 2 possible causes. The common one is that our bodies naturally increase glucose levels in the morning so that we have the energy to get up. Apart from advising that you get up as soon as you wake and do not spend time lazing in bed, then there is not much one can do about this. The second cause is having a mini hypo in the night. This depends on your medication and also timing of the last meal. The only way to find out if this is happenening is to use a CGM meter, or setting the alarm clock for the early hours then testing bgl when it goes off.