only ones i can think of that would for sure be under 10kg stock would be the 14" wheeled bikes:
The Dahon Dove (~$400SGD new) at 8KG stock and the FSIR spin 2.0 (~$620SGD new) at 7KG stock!
Both bikes should be a great ride for you, I own the fsir and it's been fun commuting with it daily between that and my Tern. I switch them around every once in awhile. The FSIR brand apparently i found out isn't a brand new stand alone brand it's actually owned by FNHON. and the parts where pretty top notch for me, reason i picked it was the unique fold and the strength of having a one piece main frame. Because of that the fold isn't any smaller than my 20" Tern Link bike in folded form but once you pick it up you'll feel a massive different picking up 7kg vs my 13.3kg Tern (it is setup with full rack and fenders and all the heavy duty commuting stuff like brooks/mks pedals etc....)
So if you want smallest fold the Dove would be better but it will be 1kg heavier because of the weld/joint in the mainframe.
14" bikes are tiny but they are very fun to ride even for daily commuting!
even long rides if the geometry is set around the same as your bigger bike you can ride really easy with it also, this is the longest single ride i took with the 14" fsir bike and it wasn't going slowly.
if you really want 16" most cheap ones would be over the limit already and the only ones i can think of is the dahon Jifo and fsir spin 2 which both are barely at the 10kg limit. 2-3 more kg you can easily feel the difference when you carry it everyday.
Did I mention on more thing with the 14" bikes if it rains you can just buy the big blue IKEA bags for $1 and put the entire bike in there and go take transit home easily. buy a second bag to cover the top and no one will even know you have a bike with you and complain.
The locals in singapore would probably be able to help with the smaller brands but this is what I have seen from the short time I was there.