Running is one of my hobbies and I have been keeping it up for 7 years. I run 2~3 times a week and I run a distance of 5~7km each time.

Although, I sometimes run 10km.

I have started running with light dumbbells in my hands, so the distance became shorter. This season is the best for a run.

The weather is great/lovely and many flowers are blooming. I'll go running tomorrow( ･`ω･´)

- Using agreeable is a little weird in this context.

Running

Running is one of my hobbies and I have been keeping it up for 7 years.

I run 2~3 times a week and with (If you want to add more details to a sentence, it is better to use the conjunction "with" because "and" is a conjunction that separates two clauses) a distance of running is 5~7km at one time usually.  (This isn't grammatically wrong but the meaning can be confusing. Running "one time" means you only did it once EVER. If you repeatedly do it, then I think "usually" is the better word.)
Although I had run sometimes 10km before, I have started running with light dumbells dumbbells in hands (You have two choices of corrections here. 1. in hand 2. in my hands. "in hands" is wrong because of the lack of an object. Either you add "my" or you change "hands" into "hand" so that the example would sound general. 1. is somewhat difficult to explain so feel free to message me if you're confused), so a (If you are aware of the noun, use "the" instead of "a." If you are referring to the noun in general, use "a.") the distance became short.

Now is (Either add a linking verb or a comma after "now" if it's the first word of the sentence) the best season for a running. (If you are aware of the noun, use "the" instead of "a." If you are referring to the noun in general, use "a.")
The weather is agreeable (suggestion: "agreeable" sounds unnatural. I think it's better to use the word "nice/pleasant/enjoyable/delightful.") and many flowers are blooming.

I'll go running tomorrow( ･`ω･´)

Hope this helps~! Running is nice and your running distance is impressive!