>lightweight, preferably small in size, and not sluggish
So I suggest Link me: Naked Browser
> Also a good UI is preferred.
Sorry, NB is not nice, was not made for that, but give it a try.
EDIT There's free version available on official website
It is because the developer is so sensitive that he blocks the entire country for the free version if he bad reviews from that said country. Not joking.
It is available on the website:
I have Firefox Focus and Naked Browser installed. Though focus looks better and blocks ads, Naked Browser is the resource-light and fast enough. Try those. Also, if like me, the free naked browser isn't available in your country, you can download it from the dev's website here http://nakedbrowser.com/android/
Linkme: Firefox Focus, Naked Browser
Naked Browser - very lightweight browser, installed size is incredible 500 KB. UI might be a bit of an acquired taste. http://nakedbrowser.com/android (if visible not on Play)
Opera Mini - does not use Webview (like for example above Naked Browser and most others), so it can be more usable in practice.
RedReader - reddit client.
Naked has a free version, it just may not be available in every country because of the dev's interesting habits. Free version apk is always available on the website.
You can't simply compare Opera Mini to pretty much any other mobile browser. When you browse the web using Firefox, Dolphin, or whatever else floats your boat, you're really viewing the actual webpage, with all the active JavaScript, CSS animations, Flash content, and whatnot.
Opera Mini does it very differently. Instead of "simply" downloading and then (not-so-simply) rendering the source files of the page you want to visit, it only sends a request to Opera servers, where the page is downloaded, all active content is removed, images' sizes are reduced, the whole result is compressed, and then sent to your device. As a result, not only you save a shitload (that is up to 96% in my experience) of data from your potential FUP limit in your data plan, but because there are no interactive elements in the compressed page you also save your phone's battery. The drawback of this that some webpages will stop working completely, unless they have an alternative mobile "lightweight" version - like m.facebook.com, m.reddit.com, docs.google.com/m, or mobile.twitter.com.
TL1DR thanks to the fact that Opera Mini only views a static page, it also saves your data plan and your phone's processing power, RAM and battery.
If your want a really lightweight Android browser, try Naked Browser. It's freakishly fast (compared to other browsers that dont't use data compression), has a minimal user interface (you could call it ugly but whatever) yet a decent amount of settings, and the app size is ~112 kB. If you open a lot of tabs and you run out of memory, it simply unloads previous tabs. However, it relies on Android's certain built-in components, which have been changed in Android 4.4 KitKat, so it might not work on this version (I'm running Android 4.1.2 and have no problems).