On the Falcon 9 FT Wikipedia page, the fully fuelled weight of Falcon 9 is only 546 300kg instead of 549,054kg as stated on SpaceX website.
Since this weight does not include a payload but it includes fairings, why would the number be 2.754 tonnes less than reported? Does this 3* tonne difference relate to propellant density? Why would they display such a static number to such a dynamic weight difference? Does anyone know what this difference could relate to exactly?
NASA Astronaut Don Pettit's Tyranny of the Rocket Equation as well as the underlying Tsiolkovsky rocket equation dictate that most of a rocket's mass when launched from Earth is propellant. Very roughly it's 90% but it varies by mission and by vehicle.
Does this 3* tonne difference relate to propellant density?
So the tl;dr might be yes, while the dry weights might be more stable (as they are for say cars), the total weight spec for rockets is mostly that of the propellants. However without the actual detailed tallies used in each case, it's almost impossible to be sure if there aren't several different part-per-thousand effects that add up to 5 parts per thousand.
The figure below is from my fairly old question Does the NK-33 engine require subcooled kerosene so cold that it turns to wax?. Sources of data are there, the script (containing the data) is at https://pastebin.com/DNqiLLb6
Roughly speaking a 30C or 30K change in temperature results in about a 10% change in density.
Your difference is about 0.5% which would correspond to less than about 2C difference in temperature for "topped-up" tanks.
Since the LOX is sub-cooled, it means that it is not at a fixed boiling point temperature, but instead the temperature (like that of the RP-1) is quite bit flexible!
In other words, a few tons here or there could depend on something as simple as the weather, or trying to squeeze a little extra propellant in for a given mission with a tight constraint on range, or where they want to land the reusable booster.
I think a difference of only 0.5% is too small to try to nail down to a fixed value.
I see several issues here.
First, the values currently given on the SpaceX website are inconsistent by themselves. 1,207,920 lb are 547,903 kg and not 549,054 kg.
Second, the Wikipedia you linked uses the current 549,054 kg value since more than 2 years. I can't find your stated 546 t anywhere in the history of the page.
Third, We know that SpaceX was working on improvements continuously. For example there is the transition from Block 4 to Block 5 taking place earlier this year. The additional weight of several tons can well be due to these changes. Note that the Falcon 9 weight was reported as 541 t before 2016 and as 505 t in 2013, i.e. it is subject to many changes.
Fourth, if you refer to the sum of total weights from the "Rocket specifications" table, it is unclear to me if any of the values contains the interstage and whether the numbers contain grid fins and landing legs on the reusable version or are for the 'pure' first stage only.
Fifth and last point: According to sources listed, the values are taken from a French space magazine and spacelaunchreport.com who put many 'estimated' and '?' in their tables, so can't be taken as definite numbers.
Wikipedia, and everyone else outside SpaceX, has to make an estimate of various specifications of the Falcon 9, because SpaceX doesn't publish much data at all, and the data they do publish have been inaccurate in the past. Estimates include:
With that many estimates, it's easy to be off by way more than 3 tons.
By the way, as of today the figure on the English Wikipedia is 549,054 kg, matching the SpaceX number.
