Hi mmbecks
I agree with the others - depending on how long you've been menopausal, how far you are into it ( re periods, frequency etc) and how old you are - whatever happens it will take more than 3 weeks for your body to acclimatise to taking this extra oestrogen.
Oestrogen does not help you sleep as such, but works to reduce and hopefully eliminate the flushes and sweats and other negative symptoms eg aching joints, that might be stopping you from sleeping.
I would not increase the dose yet, if at all. As Suzyq says - the recommended time for settling in is 3 months. The only reason not to follow this is if the progestogen in the HRT is causing adverse side effects which happens with some women and with some of the synthetic progestogens.
Hopefully you are also doing all the usual things to help maximise the chance of a good night's sleep re nightime routines etc?
Hurdity x