QUOTE:
Go to Admin Panel -> Components -> Weblinks -> Weblink Categories.

Add blogroll as new category.

Alternatively, to use existing Weblink Category (for example, <xxx>),

Go to Admin Panel -> Modules -> Site Modules

Click on BlogSidebar, In the parameters section, search for blogroll/Weblink Category. Replace "blogroll" with <xxx>.

First I got the same SQL error as stated before by davidloknl and vnative.

Then I added "blogroll" in Weblinks Category, as it was written by you.. After that I searched in bolgsidebar module the field "weblink category to use" and I wrote "blogroll" in it.

But now I get a new error at my blogroll module position, although I made it like you wrote here:
"Invalid query: Whole query: SELECT title, url FROM #__weblinks WHERE catid=161 AND published = 1"

I would appreciate, if you may help me with this matter.