In the UK it's advised LOs this age aren't weighed more frequently than every 6 months
OK, I just checked my book again and I was a little out on my ages.
At 6-12 months age it is recommended to weigh at 2 month intervals.
At 1 year it's recommended they are not weighed more than once every 3 months and not less than once every 6 months.
At 2 years it is not more than once every 6 months then at 2.5 years and then at school entry.
The clinics in the UK are freely available so it is not uncommon for mums to take their LOs for weighing more frequently sometimes even every week, I know the clinics I attended they would never tell you if you went too often, they just do the weighing and mark the chart without questioning how often you go.
My LO has gone to hospital a few times and they always weight them there regardless of when the last time of weighing was, it's so they can be accurate with medication doses and monitoring of weight gain/loss if LO becomes very poorly. These are like extra weigh ins rather than regular ones.
I don't think you are doing anything wrong, and I doubt your Lo is underweight or that there is a problem. it's totally natural to worry though.
FWIW my boy still wear 9-12 month tops and 12-18 month trousers (in leg length) even though he has turned 2 years old! His waist is the size of a new born, he fits 0-3 month baby trousers for his waist size but the length stops at his knees like shorts. I've had all his 12-18 month trousers altered at the waist to account for his small build.
Are you sure he's hungry in the night? Do you give water in the day and before sleep?
I had a short spell of DS asking for food just before BT (that is after having had dinner to his fill then supper to his fill) and was advised by BWers to increase his protein intake. He didn't take much protein at that time, so I changed up his meals and made breakfast a protein meal because he is so hungry at breakfast that he is likely to take a good portion of protein then. Because he had that, he was no longer asking for food before bed. Breakfast seems a long way from BT but the calorie intake across the day is what counts for a 1year old rather than what they eat right before BT (like a new born). overall his diet improved too because I couldn't rely on him always having protein at other times of the day, he would often choose veg or carbs from his plate instead.