The Earth doesn’t have a “weight”, but it does have a mass. For the purposes of your question the meaning is the same. No, the mass of the Earth changes over time.
Meteors hit the Earth and are added to our mass. (about 44 tonnes a day).
Gas, mostly hydrogen floats high enough to be lost to the solar wind so we lose a bit of mass. (About 90 tonnes a day)
If you’re really counting details, some space probes are launched to never return.
In total we generally are losing mass day-by-day, but not much in the scheme of things, even over 100’s of millions of years.
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