What is the difference btween 看样子 and 看起来
From the comment by @user6065


Similarities and differences of '看来', '看起来' and '看样子'

Similarities:


They are all conjunctions, used to make judgements or predictions based on a specific situation.
They could be used at the beginning of a sentence.
They are interchangeable sometimes
Examples:


天一下子阴了，看来(看起来/看样子)要下大雨了。


It is cloudy all of a sudden, looks like it is about to rain.

赵娜老打哈欠，看来(看起来/看样子)昨天晚上没睡好。


Zhao Na keeps yawning, looks like she didn't sleep well last night.

雨下个不停，看起来(看来/看样子)我们这几天去不成海边了。


It is still raining, looks like we can't go to the seaside in a few days.

看起来(看来/看样子)，这条马路到年底也修不好。


Looks like this road won't get fixed by the end of year.

杰克笑嘻嘻得走过来，看样子(看来/看起来)他今天心情不错。


Jack is coming with smile on his face, looks like he is feeling good today.

王经理一直没出声，看样子(看来/看起来)他对这个计划并不满意。


Mr.Wang didn't say anything, it looks like he is not satisfied with this plan.




Differences:


"看来" is to represent the inference by analysis (little bit). While "看起来" and "看样子" represent the inference more obviously, such as the inference easily made according to appearance. 
"看来" is only used before Subject most of the time. While "看起来" and "看样子" could be used before or after Subject.
"看来" could be used in these structures: "从...看来", "在...看来", "由此看来", "照我看来", which refer to get the inference via different perspectives. "看起来" and "看样子" cannot be used in these structures.
Examples:


他看起来(看样子)像个40多岁的中年人，哪像个20多岁的小伙子？


He looks like around 40 years old. How could he look like a 20-year-old guy?

这些花看起来(看样子)像是真的一样，其实是假的。


These flowers looks like authentic, but they are artificial.

他看样子(看起来)很老实，其实狡猾得要命。


He looks like honest, but he is cunning.

这些菜看样子(看起来)就很好吃，我今天要多吃几碗饭。


These dishes looks tasty. I would like to have more today.