力求= make every effort to; do one's best to; strive to 盡己所能(尽己所能)= do my best 力求 is a verb 盡己所能(尽己所能) is an adjective

actually ,the two expressons means the same. they both means make very effort to ,try one't best to . but 力求 is more often used to express "make every effort to (do some thing/make../let)" 尽已所能 is more often used to express "make very effort" here are some examples: 他仔细检查设计图，力求完美。he carefully checked over the design drawing,making every effort to make the drawing perfect. 我们一定要尽已所能，帮助别人。we should make very effort , to help others who are in trouble. Both of them are formal .so your example seems to be not so good. you should say , 我尽量减肥/我想尽办法去减肥 i try my best to lose weight

"我尽量减肥/我想尽办法去减肥" 比 "我尽己所能减肥" 更常见。后者读起来比较文诌诌的.

差不多，后者更给力点。

谢谢bebe:-)