Question: I normally write using the *American* English forms, but for some particular words, I tend to naturally write it in the *British* manner (like with the word *favourite* rather than *favorite*).

Is it wrong to mix both styles? If not \*wrong\*, does it looks weird?

Answer: 
Sure. For example, [Canadian English](http://en.wikipedia.org/wiki/Canadian_English#Spelling) has standard spellings that are derived from both British and American influences.

> 
> Canadian spelling of the English language combines British and American conventions.
> 
> 
> * French-derived words retain British spellings (*colour* or *centre*). While the United States uses the Anglo-French spelling *defense* or *offense* (noun), Canadians use the British spellings *defence* and *offence* (*defensive* and *offensive* are universal).
> * Use of *curb* and *tire* in contrast to British English *kerb* and *tyre*.
> * Words ending in *-ise* use "-ize" after the US English convention.
> * Some nouns take *-ice* while matching verbs take *-ise*, as with practice and *practise*, *licence* and *license*.
> * Canadian spelling can retain the British practice of doubling consonants when adding suffixes to words even when the final syllable (before the suffix) is not stressed, as with *travelled*, *counselling*, and *controllable*.)
> 
> 
> 

The preferred Canadian spelling is *favourite*. That is the form that would be chosen in formal publications. However, in practice, Canadians tolerate both British and American spellings with little fuss, and *favorite* would also be commonly seen.

Note, however, that there are a few words for which Canadians do have a definite spelling preference. *Kerb* and *tyre* would look markedly out of place in Canada. I speculate that it's because they are more modern concepts, and therefore subjected more to American influence. Also, there is a popular chain of hardware stores called [Canadian Tire](http://www.canadiantire.ca/en.html), which would make *tyre* un-Canadian.

Caution: "Official" usage doesn't always paint an accurate picture of common Canadian English usage. For example, Transport Canada (government) regulations all use [*aeroplane*](http://search-recherche.tc.gc.ca/search.aspx?q=aeroplane&cn-search-submit=Search), while the CBC (media) and everyone else in Canada use [*airplane*](http://www.cbc.ca/gsa/?q=airplane).
It must be noted, to add to the other answers, that some official exams will penalise you for mixing. For example, Cambridge (British English) will probably tolerate American English if you are consistent, but certainly penalise you if you mix them. I have also known of professors in the UK that consider American-spelled words an orthographic mistake, and therefore lower your grade for it (and being harsh!).