Correct

轻视 vs 看不起

/ qīngshì vs kànbuqǐ /
Strokes

Definition

轻视 is a Verb, 看不起 is a Verb phrase, which both means [look down upon; underestimate; disdain].

Example

轻视 is more literary than 看不起 and can function as the object of verbs like 受到, 遭受, etc; 看不起 is more colloquial and cannot function as the object.
In examples ① and ② 轻视 is used and not 看不起. In example ③, either word can be used.
1
Zhè
gōngzuò
工作
hěn
zhòngyào
重要
  
,
néng
qīngshì
轻视
  

The job is of importance,so take it seriously.

2
Yóu
由于
chūshēn
出身
pínhán
贫寒
  
,
jīngcháng
经常
shòudào
受到
mǒuxiē
某些
rén
de
qīngshì
轻视
  

He is often looked down upon by some people because of his poor family background.

3
néng
kànbu
看不起
  
(
qīngshì
轻视
  
)
自己
  
,
yīnwèi
因为
xìn
自信
shì
chénggōng
成功
de
qián
前提
  

You should not look down upon yourself for confidence is the key to success.

When applied to one's attitude, 看不起 means "to 觉得……不如自己 deem someone as below oneself and 羞与为伍 feel ashamed to be in his company"; in this sense, 轻视 is not used.
4
Duì
cánrén
残疾人
  
,
men
我们
yīnggāi
应该
kànbu
看不起
men
他们
  
,
ér
yīnggāi
应该
zūnzhòng
尊重
men
他们
  
,
bāngzhù
帮助
men
他们
  

We shouldn't look down upon the disabled, but respect and help them.

5
guàn
一贯
shì
zhī
shuō
zuò
  
,
tóngxué
同学
men
dōu
kànbu
看不起
  

He was disdained by his classmates for his usual empty talks without any deed.