with the melting of the ice over land and loss of weight on that part of the crust result in seismic activity?

What you are talking about is isostatic rebound. Yes there would be some minor shallow earth tremors as the land begins to raise. The rising of land is happening now with Scotland still raising after the last Ice Age (Though I'd hate to attribute last weeks earthquake to it). There is a secondary problem though with all the melt water. The water can get into existing faults and make them unstable and can even get into volcanic systems causing eruptions. I think something like this occurred round the Med at the end of the last Ice Age.

Any effect will be quite small. Why?

- Ice is light anyway

- Some water is incoproated into cloud cover

- In a lot of cases (e.g. the Alps), the source (glaciers) and sink (ocean) are on the same plate (Eurasion), meaning the difference will be even smaller.

Trust me, if you see significant amounts of ice melting (e.g. from the greenland and antartica ice caps), seismic activity will be the last thing on our minds.

I don't think it would be seismic activity - because that is rooted within the tectonic plates (much deeper)

But there could be earth movements certainly

Yes. It is called isostatic rebound. The quakes would likely be very small.

I think it's called isostosy that applies in these circumstances.