Difference between 儘量 and 盡量?
'儘' in '儘量' has the 亻 Radical, denote 'human effort'


  儘量 :'to the best of one's ability' ; 'as far as possible' (in term of human effort)
  
  Do not confuse with 盡量 which is different in form, reading, and meaning.


~


  盡量 : reach the limit (drink or eat); to the full
  
  Do not confuse with 儘量 which is different in form, reading, and meaning.


Example:


When you say '我會儘量給他貸款' , you mean: 'I (personally) will do my best to give him a loan' (to the best of you ability to secure a loan for him)
When you say '我會盡量給他貸款', you mean: " I will give him the maximum amount in loan'. (if the bank only authorizes you to lent out loans no bigger than $5000, then $5000 loan is the limit) 


Another example:


儘量投放物資 - do one's best to deliver supplies
盡量投放物資 - deliver maximum amount of supplies until it is exhausted



  尽 is the simplified form for both 盡 and 儘.


Which mean in Mainland China, 儘量 and 盡量 are both written as 尽量, but their pinyin are different depend on which meaning you are using.