there are many well written and repeated discussions on fill tank part or full.
In the overall picture driving style and maintenance of the vehicle will give bigger returns.
On fil part/full here is a typical article
"However, the truth to our burning question is that a full tank only accounts for around 5% of the car's total weight. By reducing your tank to half its maximum level, it means you will only save around 2.5% in total weight. This will give you only a very small saving in terms of fuel economy.
Regardless, It is still recommended that you fill the tank up to the top when you visit the petrol station as this will ultimately save you time as you won’t need to make so many trips.
For example, if you fill the tank up and this lasts a month, that’s just one trip. If you top up periodically, you could make three or four visits over the course of the month costing you time. And you know what they say? Time is money!
Ultimately, the difference you save in terms of the weight of the tank is minuscule compared to the amount of time you will save and the mileage of filling up each time."