Task1 (half of it)

The graph illustrates the quantity of goods by weight which were transported in the UK by four measures (road, water, rail and pipeline) from 1974 to 2002. Units are measured in million tonnes.

Overall, the amount of goods transported by road, water and pipeline increased from 1974 to 2002, whereas by rail, it remained almost the same.

'amount of goods' is ok. But if you say 'quantity of goods by weight' it is clearer that thee goods are being measured by weight, not actually counting individual items. But I have a question for you, what sort of goods are displayed on the graph? This will determine the best way to paraphrase it. 'materials' might be a better word, for example, if the 'goods' are raw materials like plastics, wool, coal, and so on.

Writing for IELTS task 1

HAPPY NEW YEAR EVERYONE!
あけましておめでとうございます。

I'm working on IELTS writing task1, and I need your help to correct my sentences.
私は今、IELTSのライディングに取り組んでいて、文章チェックのためにあなたの助けが必要です。

Task1 (half of it)

The graph illustrated the amount of goods which were transported in UK by four measures (road, water, rail and pipeline) from 1974 to 2002. Units are measured in million tonnes.

The graph illustrates the amount of goods that were transported in the UK by four different kinds of transportation such as roads, water, rail, and pipeline from 1974 to 2002. Units are measured by one million tons.

Overall, the amount of goods transported by road, water and pipeline ended the period up compared to it in1974 to in 2002 whereas by rail, it was almost the same.

Overall, the amount of goods transported by road, water, and pipeline ended up increasing from 1974 to 2002 whereas by rail, it was almost the same. 

Question
I want to paraphrase "the amount of goods tra ported". Do you have any good suggestions?

You can use "the merchandise transported" or "the amount of goods transported" "the number of goods transported" things like that. When using the word "goods" for any product (merchandise) it can be used in a number of ways. If you want to sound more professional use the words "product(s)" or "merchandise." "Goods" is sort of like an informal way of speaking. Also, in the last sentence I corrected, I used an extra comma when I separated "road, water, and pipeline." This is another annoying thing in English. The way you used commas are correct and the way I used them are correct. I can't remember what it's called, but there is some book out there that is the official way to use commas and both of these ways have been called correct. However, since I'm seeing more professionals use commas in the way that you used them, I would suggest you stick to that way. The way I use commas is how I learned when I first started writing English as a kid. I hope this was helpful and not too much information!

Writing for IELTS task 1

HAPPY NEW YEAR EVERYONE!
あけましておめでとうございます。

I'm working on IELTS writing task1, and I need your help to correct my sentences.
私は今、IELTSのライディングに取り組んでいて、文章チェックのためにあなたの助けが必要です。

Task1 (half of it)

The graph illustrates (could use either, but this makes more sense if you are explaining what the graph is to someone) the amount of goods which were transported in the UK, by four methods of transport (road, water, rail and pipeline) from 1974 to 2002. Each unit in the graph represents 1 million tonnes.

Overall, the amount of goods transported by road, water and pipeline ended the period up compared to it in 1974 to in 2002 whereas by rail, it was almost the same.

This last bit doesn't make much sense without the graph involved. I'm guessing your trying to say this. The road, water and pipeline methods of transporting goods increased during the period between 1974 to 2002, whereas by rail, it was almost the same.