Blathering's correction is excellent and I can do no better.  However, I would like to change some wording, starting with the title.  "The Joy Of Jogging" would be a nicer title.  I prefer the word "jogging" than "running".  What I am doing now is a step by step process in which I do during translation from one language to another.  Literal translation is in blue and those in red are what a native speaker would normally use in this setting. If none, then whatever is in blue can also be used normally.  After I am done, I put all the English sentences together and see if there are more polishing to be done.

自从我发现我体重超标后, Ever since I discovered that my weight has exceeded the optimal level, Ever since I discovered I was overweight,

我坚持每天跑步1小时已有20多天，I persist that I will spend one hour each day in jogging which I have done for 20 days now.  For 20 days now, I persisted (had made sure) that I will be spending an hour each day to jog.

我现在很享受长跑. Now I enjoy long distance jogging.

跑步时专注地呼吸, When jogging, I concentrate mainly (or mostly) on breathing.

忘掉其他所有的事情，Forget all other things.

没有工作，No work,

没有烦恼，No vexing problems,

我的世界突然变得很安静。My world has suddenly changed to quietness. My world has suddenly become quiet.

在我最累的时候，At the moment when I am most tired, When I am exhausted,

我想要更多的氧气，I think I wanted even more oxygen,

但却发现即使我尽量的张大嘴, Even though when I opened my mouth as wide as I can,

还是很难呼吸。Still difficult to breathe. Still I have difficulty in breathing,

我没有停下，I did not stop,

而是继续加速跑, Still continue and quicken my jog, instead, I continue to increase my jogging speed.

直到我感觉自己就要倒下。Straight till I felt like dropping down.  Until I felt like collapsing.

真希望我能尽快恢复到健康的体重。Really I wish I can recover my body health fast. In earnest, I wish I can return to my physical health quickly (as soon as possible).

Ever since I discovered I was overweight, for 20 days now, I persisted(had made sure) that I will be spending an hour each day to jog.  Now I enjoy long distance jogging.  When Jogging, I concentrate mainly (or mostly) on breathing.Forget all other things, No vexing problems,My world has suddenly changed to quietness. My world has suddenly become quiet.When I am exhausted, I think I wanted even more oxygen, instead, I continue to increase my jogging speed.Until I felt like collapsing. In earnest, I wish I can return to my physical health as soon as possible.

The Joy Of Jogging

Ever since I had discovered that I was overweight, for 20 days now, I had made sure that I will be jogging an hour each day.  I have grown to enjoy long distance jogging.  I concentrate mostly on my breathing when I jog and forget everthing else.  With no vexing problems to deal with, my world has suddenly turned into a place of quietude.  When I am exhausted, I feel like I needed more oxygen.  Instead of stopping, I continued to increase my speed until I feel like collapsing.  In all earnesty and haste, I wish I can regain my physical health.

Enjoy Running享受跑步

I have been keeping running for one hour per day for 20 days after I realised I was over weight, and I find I enjoy long distance running so much now. In running time, I just focus on my breath, forget everything else, no work, no trouble, my world suddenly become so quiet. At the most tired moment, I want more oxygen but I find it is very hard to breathe even though I open my mouth as large as possible. I speed up instead of stopping, untill I feel I am going to fall down. I realy hope I can go back to healthy weight range as soon as possible.
自从我发现我体重超标后，我坚持每天跑步1小时已有20多天，我现在很享受长跑。跑步时专注地呼吸，忘掉其他所有的事情，没有工作，没有烦恼，我的世界突然变得很安静。在我最累的时候，我想要更多的氧气，但却发现即使我尽量的张大嘴，还是很难呼吸。我没有停下，而是继续加速跑，直到我感觉自己就要倒下。真希望我能尽快恢复到健康的体重。

Enjoy Running享受跑步

I have been 1） keeping running for one hour per day one hour every day for 20 days after I realised I was 2) overweight (一起）, and I find I enjoy long distance running so much now.  2）While running In running time, I just focus on 3) breathing my breath and forget everything else: no work, no trouble, and my world suddenly becomes so quiet. 4) At the moment when I am most tiredAt the most tired moment, I want more oxygen but I find it is very hard to breathe even though I open my mouth as 5) widely large as possible. I speed up instead of stopping, 6) (and keep on going) untill I feel I am going to fall down. I realy hope I can 7) return go back to a healthy weight range as soon as possible.

自从我发现我体重超标后，我坚持每天跑步1小时已有20多天，我现在很享受长跑。跑步时专注地呼吸，忘掉其他所有的事情，没有工作，没有烦恼，我的世界突然变得很安静。在我最累的时候，我想要更多的氧气，但却发现即使我尽量的张大嘴，还是很难呼吸。我没有停下，而是继续加速跑，直到我感觉自己就要倒下。真希望我能尽快恢复到健康的体重。

加油！  跑步的確是又健康又輕鬆的活動。 

1） 英文通常不會連續用兩個"-ing"的動詞。  另外個選擇是 “I have been continuously running..."

2) In running time這個句子不通； 你該講的是While running(跑步的時候）

5) Wide and big意思不同；嘴巴張大 is to open your mouth widely (ly表示副詞).

比如說： The whale opened its mouth widely to swallow the fisherman.

金魚把嘴巴張大，要吞進漁夫。

^__^.