Sandesh

Lightweight Live Ajax Search plugin enables AJAX powered live search. Lightweight and provides a shortcode to display live search input box anywhere. You can place a shortcode wherever you want. Fully optimized and easy to use plugin.
<h3>How to use?</h3>
** Replace theme’s search form **
If you want to replace them’s search form, then it is a plug and play feature.
<ol>
<li>Go to Setings->Live Search</li>
<li>Enable Replace Theme’s Search Form option</li>
<li>Select the post types you want to allow for a search</li>
<li>Save it.</li>
</ol>
All instance of your theme’s search will replace with Live Ajax Search
** Use shortcode ** 
In some cases, if you do not want to replace theme’s search form, copy the shortcode and paste it anywhere you want. You have full flexibility on it.
<ol>
<li>Go to Setings->Live Search</li>
<li>Disable Replace Theme’s Search Form option</li>
<li>Select the post types you want to allow for a search</li>
<li>Save and Then Copy the shortcode and place it anywhere you want.</li>
</ol>

Lightweight Live Ajax Search

Live Ajax based search functionality. Lightweight and provides a shortcode to display live search input box anywhere.

myselfko

Simple and lightweight widget for displaying weather data and forecast from Weather Underground (www.wunderground.com).
Plugin saves a local copy of data for faster and more optimal running. 
You need a Wunderground API key, which you can get here http://www.wunderground.com/weather/api/.
Features:
<li>simple and lightweight</li>
<li>multilanguage (currently supported: english, german, italian, slovene)</li>
<li>easy for translating</li>
<li>metric and imperial units</li>
<li>user can define own refreshing interval in minutes</li>
<li>no need for own weather icons, plugin automatically download them from Wunderground</li>

EasyWeather widget

Simple and lightweight widget for displaying weather data and forecast from Weather Underground (www.wunderground.com).

Lightweight Live Ajax Search vs EasyWeather widget