people don't tend to look out for petite asian girls tugging 2 suitcases and run off with one of the suitcases, not very often anyway.
I'm sure that if you dig deep enough and look under enough rocks on Google or your search engine of choice you can find an instance of such a thing, or at least an account - confirmed in truth or not - of something similar.
Steal a phone, yes happens all the time in bars and to vulnerable people, but whole suitcases - no.
That shouldn't be a worry unless you wander off and leave one or more unattended.
More important is the cases being too big for you to wrangle. Nobody is going to help you, most likely, so being able to wrangle what you brung is critical.
Take everything you want to bring and put the stuff into the very big suitcase or 2 just large suitcases (neatness doesn't count much at the moment), sit on it to close it, and grab a local bus at home or in town, get the cases down the aisle, go a few stops then get off and drag the case(s) two or three times around a couple of busy city blocks, then back on the bus and home.
Then take out half of what you put in - those things that are essential but after the last experience are suddenly much less essential.
Oh yes, before you open them when you get home carry them up 3 flights of stairs.
If you can't do all that, you have more than you can handle.
Either leave much at home or find a strong friend to carry and lift for you on the trip in February. Have them come back to you in June.
By the way, possibly second only to Paris, I've never seen so many stairs as in London - usually stairs without a step free alternative.
In both the London Underground and the Paris Métro you will go down stairs so that you can go immediately up more, or vice versa.