What is the difference between 敬仰 and 瞧得起
'敬仰' means 'respect and admire' ; 'look up to'.
If you say that you 敬仰 someone, you are humbling yourself.
'瞧得起‘  means 'consider worthy'
If you say you 瞧得起 someone, you are putting yourself in the position of judging that someone's worthiness (and in the position of granting favors to him or her) ;  you thanks someone for 瞧得起你 (consider you worthy) to show your humbleness.

因为他是你弟弟，当然他瞧得起你
... why '瞧得起’ is unfriendly, derogatory.

It is not unfriendly or derogatory, just improper in certain situations. It is perfectly acceptable to say: &quot;your boss promotes you because he 瞧得起你&quot;. It is also fine to say: &quot; A big movie star 瞧得起你 because he invited you to his party.&quot;
A younger brother is not in the position of judging his older brother's worthiness. Therefore, 瞧得起 is an improper term to be used in this instance.
Even for an older brother, it is still not right to say someone 瞧得起 his younger brother-- Brothers are expected to consider each others worthy by default.
Side notes:
敬仰 = 尊敬(respect)+ 仰慕(admire)
The opposite of 瞧得起 (consider worthy/ look favorably upon) is 瞧不起 (consider not worthy/ look down upon)