The really curved ones are noticeably heavier than the usual diamond frame. What about the ones that use a more aggressive slope, rather than the curve?

M.

Pretty much any non-triangle frame is going to need extra material to make up the difference in strength. The more of a triangle,the less extra material you'll need. Also,the frame material is going to make a big difference.

Stepthrough frames are often heavy because they are not made light. I have seen step-thu frames made from Reynolds butted steel and they are reasonable, but even these were made to touring, not racing grade.
There is a carbon fibre step-thru/mixte style frame. Carbon fibre is probably better suited to this style than metal tubing.

Don't fixate on weight, though. Light is always nice, but the difference between a heavy frame and a light one is likely to be just a few pounds. My weight varies that much from day to day, and two full water bottles weigh three pounds. If you find something that feels right, don't let a small weight difference scare you off.

Yeah. Check out quality mixte style frames. They are usually only a little heavier than comparable double diamond frames of similar quality:
https://www.google.com/search?q=mixt...w=1516&bih=959

the difference in weight between a good quality mens frame
and a step through frame of identical construction
for instance
the difference between mens and ladies frames of the same make and model
is usually not enough to give a second thought

there seem to be fewer and fewer good quality step through frames
as the years go on
though
and the above statement about weight does not necessarily apply
to comfort bikes and city bikes

but i have seen some very nice light step through frames in my life
from manufacturers like fuji and univega