Nothing quite as small that I'm aware of; it's not that much lighter as today's best, with the better battery option. The dimensions and weight I see for the Vaio X are:
- 11.0 x 7.3 x 0.6
- 1.4lb with smallest batter, 2.2lb with extended battery

Most comparable high-profile models:
- Macbook Retina (11 x 7.7 x 0.4-0.5", 2.0lb; slow Core m3 or slowish Core m5)
- Surface Pro 4 (11.5 x 7.9 x 0.33" thickness w/o keyboard, 1.7lb w/o keyboard; add .13" and 0.4lb for the touch keyboard; choice of slow m3 or fast i5 processor.)
- Dell XPS 13 (9360, Kaby Lake, 12x7.9x 0.3-0.6", 2.7lb, fast-ish i3 or fast i5 processor)

There are several Surface Pro clones -- e.g. the XPS 12 and Latitude 7275 from Dell. Dimensions and weight tend to be a little heavier, but similar overall.

While the current Core m processors are pretty slow, it's worth a reality check on the Vaio X (and other Atom-based, 2009-vintage netbooks.) Modern machines are off the scale by comparison.

The Atom Z550 in the Vaio X has a passmark score of 381, and the Vaio X has a reported geekbench score of 963.

By comparison, the slowest laptop processors I'd consider not simply slowing away have passmark scores close to 1200 (Core 2 T7200), and that's three years older than the Atom. The slowest processors I'd consider using personally (i5-4200Y) has a passmark of about 2350.

By comparison, the slowest machine there (the Core m3 versions of the Surface Pro 4) has a passmark just over 3000.

Or to look at Geekbench, the Core m3 machines make about 2549 on single core or 5164 on dual core. A decent cheap-ish new smart phone, the Honor 5X (a $199 phone!) has a geekbench of ~680 on one core (nearly as fast as the Vaio on only one core) or ~2900 on multiple cores.

IOW, any decent machine from the past ~3 years is going to be insanely faster than the Vaio. Before the Haswell (2013) generation processors, there wasn't really a decent super-low-power processor, and the lightest machines were going to be closer to 3lbs, but since then the Core i5-4xxxY and the Core m and m5 processors that replaced them have been pretty darn good.

Even today's Atoms intended for "tablets" are really fast compared to the one in the Vaio X. "Toy" 8" tablets like the Dell Venue Pro 8" (5855; 0.37” x 5.12” x Depth: 8.5” ; 0.83lb) will outperform the Vaio X by about 4x (similar single-threaded performance ,but quad core.)

Might also look at some 11" Chromebooks...