What is the total weight of the Earth?

It would be more proper to ask, "What is the mass of the earth?"

The quick answer is approximately 6,000,000,000,000,000,000,000,000 kilograms.

Earth's mass is 6.580 sextillion tons according to the World Book of Facts 2003 edition.

Mass and weight are different. Mass is the amount of matter in an object. Unlike weight, it is not affected by location. Weight is the effect of gravity on mass.

Earth is increasing in mass by many thousands of tons daily by the daily accretion of extraterrestrial meteorites and meteor dust.

Jens Gundlach and Stephen Merkowitz from the University of Washington, US have found that the Earth weighs in at 5.972 sextillion Metric Tons.

http://www.washington.edu/news/2000/04/29/uw-physicists-find-more-precise-gravity-number-and-weigh-the-earth/

The Earth's actual weight:
5,972,000,000,000,000,000,000 Metric Tons or, 5,877,681,383,000,000,000,000 Long Tons (UK) or, 6,479,034,670,000,000,000,000 Short Tons (US) or,
12,958,069,340,000,000,000,000 Pounds (US)

The earth gains between 10 and 1,000 tons of mass in the form of dust each day. On average, only two meteors about the size of an open hand hit the earth each day. With that figure, you would think the earth would gain so much mass over hundreds of millions of years it would eventually spin out of the solar system. Actually, that amount of mass is such an infinitesimal amount to the size of the earth.

Even after one million years with 1000 tons each day = 365,000,000,000 tons, you still need 10 more zeros to even make 1%. If the earth gains 1% in mass it will move 1% further from the sun