As far as I am aware, you should have between 5-15 syns per day REGARDLESS of what your start weight is.
It doesn't say anywhere in my book (which I got brand new in January) that the syn allowance depends on your weight, and my consultant has never mentioned anything on the subject either.
The whole point of the syns is so you can have foods/drinks that you ENJOY that are not free to ensure you have satisfaction with your diet and therefore means you are less likely to completely go off-plan.
Remember if you look at it calorie-wise (And I know SW isn't about calorie counting) but the full 15 syns equals 300 calories, and based on an average person's daily calorie allowance being 2000 per day (depending on variables) then the entire syn allowance only makes up 15% of that.
I personally think that it varies from person to person and you should have your full 15 in the first few weeks, and in the event that you are unhappy with your losses, you can then take a look at how the plan is working for you and how it may need to be tweaked.
And if the losses aren't what you would envisage, the syns are not always to blame. It could be, for example, that you are doing EE and not having enough superfree, having unreasonably large portions, etc. That's why in my opinion it's important to keep a diary so you and your consultant can work together to ensure the balance is right for you.