Putting aside the question of whether it's grammatical, the problem here is not with the present continuous. Because you're using it, your audience will likely assume you plan to continue taking it easy on future weekends, and you expect to like that too. It sounds like that's what you want to say.
That said, "I'm liking" is very awkward to my eyes. By contrast, "I'm enjoying" sounds normal to me. I can't explain the linguistic difference and am inclined to chalk it off as just another quirk of English idiom.
I do think nearly all fluent speakers would understand your "I'm liking to take it easy on the weekend" the way you intend it, but I also think it would mark you as an English student rather than a fluent speaker.
For what it's worth, a quick Google search of either "I'm liking" or "I'm enjoying" returns discussions about proper usage (probably including this one soon). But aside from those, the former is mostly in titles or other abnormal usage, while the latter returns more "organic" results.
I agree with those commenters that prefer the gerund "taking" over the infinitive "to take". Again I can't explain why - I just think one is more common and thus received more easily.
As an additional note, the choice of "the weekend" versus "weekends" may be important regardless of the verb. Especially if it is currently a weekend, your audience might assume you meant that you were specifically enjoying this particular weekend. Whereas "on weekends" would imply that you've taken it easy on at least 2 or 3 weekends recently, and liked it. And because you're using the present continuous, we'd assume you plan to continue taking it easy next weekend, and expect to like that too.
Another option is to use the past continuous, which might be more common in English. It would have a very slightly different connotation here. "I've been enjoying taking it easy on weekends" has basically the same meaning as my previous suggestion, but without implying so strongly that you intend to continue your taking it easy.
Since people generally try to keep doing things they enjoy, we might assume that anyway so the distinction is very small for this example. On the other hand, if the next sentence were "But the hurricane wrecked my trees so I'll have to clean that up.", the past continuous might be more appropriate. After all, you won't be taking it easy this weekend - you'll be cleaning up.
Putting it all together, I think "I'm enjoying taking it easy on weekends" is the most natural way to say what I think you mean.