The information I get from the Internet basically agree that わりと and わりに can
be used interchangeably as a 逆接, as shown in the below sentence,

> あの人は沢山食べるけど、体は **わりと** 小さい。＝あの人は沢山食べる **わりに** 、体は小さい。

But I hear the sentence from here: 0:43 @
<https://www.youtube.com/watch?v=cW42unEZ6CQ>

> たくさん食べる人は普通は、 **わりと** 体が大きいですよね。

I hazard a guess that here わりと means "comparatively", and "わりに" cannot be used
here.

And the dictionary also says わり and わりあい are synonyms, but I am not sure if it
is ok to say

> たくさん食べる人は普通は、 **わりあいと** 体が大きいです(よね)。
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word-choice
The difference between わりと and わりに
わりに and わりと are not always interchangeable because they are slightly different
in terms of the nuance, though they both signify 逆接.

わりに emphasizes some property of the subject, using another property that
usually affects the said property in an adverse manner.

Take an example:

> 彼は毎日ラーメンを食べるわりに健康だ。

In this sentence, the health of the subject is emphasized by presenting the
fact that he eats ramen every day, which usually has a negative effect on the
health.

This is sometimes incompatible with わりと, which emphasizes some property
comparing the subject to the average.

Take an example:

> 彼は50代にしてはわりと若く見える。

In this sentence, the subject is described to look younger than an average
person in his/her 50s.

One can use わりに in this case:

> 彼は50代のわりに若く見える。

The replacement is possible because "the group from which the average person
is chosen" is explicitly present. The average person in his/her 50s has an
adverse property, namely the age, that affects the appearance in an adverse
manner.

The sentence in question:

> たくさん食べる人普通は、わりと体が大きいですよね。

does not state to which average the physique of the person should be compared.
In such a case the use of わりに is not possible because you do not know which
adverse property to present.

As for your second question, わり in わりと should not be confused with the noun
わり(proportion). They are simply different words, although I believe they have
similar origins.
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> たくさん食べる人は普通は、 **わりと** 体が大きいです。  
>  たくさん食べる人は普通は、 **わりに** 体が大きいです。

Both sound fine to me.  
Both [割]{わり}と and 割に can mean "relatively/comparatively", "fairly", or
"unexpectedly" depending on the context.

割と sounds more colloquial than 割に, just as the pairs 意外と/意外に, 自然と/自然に,
やたらと/やたらに. (cf. [Is there any difference between 意外に and
意外と?](https://japanese.stackexchange.com/q/2714/9831) / [What does 意外と
mean?](https://japanese.stackexchange.com/q/3601/9831) / [difference between
しきりに or しきりと?](https://japanese.stackexchange.com/q/47817/9831) )

Similarly, you can say:

> あの人は沢山食べるけど、体はわり **と** 小さい。(← わりと is an adverb. See [わりと in
> デジタル大辞泉](https://dictionary.goo.ne.jp/jn/238823/meaning/m0u/%E5%89%B2%E3%81%A8/))  
>  あの人は沢山食べるけど、体はわり **に** 小さい。(← わりに is an adverb. See [わりに in
> デジタル大辞泉](https://dictionary.goo.ne.jp/jn/238826/meaning/m0u/%E5%89%B2%E3%81%AB/))  
>  あの人は沢山食べるわり **に** 、体は小さい。(← わり in ～～わりに is a noun. See [わり #5 in
> デジタル大辞泉](https://dictionary.goo.ne.jp/jn/238763/meaning/m0u/%E3%82%8F%E3%82%8A/))

... but not あの人は沢山食べるわり **と** 、体は小さい since the adverb わりと cannot be used with
連体修飾語句 (attributive modifier). When used with 連体修飾語句, the 割 in 割に is a noun.

* * *

[割合]{わりあい} is originally a noun, as you may know. You might more often see it
used as a noun, but it is an adverb, too:

> わりあい【割合】  
>  ［名詞］  
>  ・・・  
>  **［副詞］** 他の物事や場合に比べてそれらの程度を超えているさま。比較的。 **割に** 。 「部屋は **割合に** きれいだ」「
> **割合（と）** やさしい問題」  
>
> ([デジタル大辞泉](https://dictionary.goo.ne.jp/jn/238771/meaning/m0u/%E3%82%8F%E3%82%8A%E3%81%82%E3%81%84/))

So you can use わりあい this way in your example:

> たくさん食べる人は普通は、 **わりあい** 体が大きいです。  
>  たくさん食べる人は普通は、 **わりあいに** 体が大きいです。  
>  たくさん食べる人は普通は、 **わりあいと** 体が大きいです。(← more colloquial)

* * *
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