わり

わりに is a very useful word, but can be a bit confusing. 割り is the ます stem Noun form of 割る, a verb meaning “to split” or “to divide”.
It is usually written as 割 but may be written as 割り. (割 is apparently “more” correct, as least when used as a noun/adverb).

Suffix わり

~わり
~Discount

わり as a suffix means “discount”. You can think of it is an abbreviation of ”割引” (Percentage off). 

• 早割 – Early bird discount.
• 団体割 – Group discount.

*Fun fact, 早割 is apparently trademarked or something, and the hotel I worked at was not allowed to say “早割” to advertise an early bird discount. We got calls about this on multiple different online booking sites. 

As a counter

割
10%

割(わり) is a counter that is used to count 10%s. Yes, by 10s.
1割 is 10%, ２割 is 20%, etc.

• 仕事の6割はここで行われている。- About 60% of the work is done is performed here.
• 給料の7割は家賃や光熱費に使われる – About 70% of my paycheck is used for rent and utilities.
• 人の約1割は左利きだ – About 10% of people are left handed.

Please note that while you may say 10割, you will probably not say 0割, nor anything over 10.

わりに

割に・割と
Relatively

わりに is a noun + に (Adverbial に）meaning Relatively or Comparatively. This will sometimes appear as 割と, although originally only 割りに was considered correct. （Source)
割りに/と qualifies a statement as a comparison to something else. 

• このかばんは割と安い – This bag is relatively cheap (Comparatively cheap).
• このホテルは割りに高い – This hotel is relatively expensive. (Compared to others).
• 彼は割りと優しい人だ – He is a relatively nice person. (Comparatively nice)
  
  

のわりに

のわりに
Disproportional to X

Another variation of this is のわりに. When modified by a noun (or verb), you may not use と instead of に.
This phrase typically expresses contrary information, as it relates to something else. 
This is very commonly used with 年 (とし), so much so that you can practically learn it as a phrase. 
This phrase also frequently adds the comparative は to become のわりには . (see also には)

• 年の割には賢い。- Clever for their age. (Disproportionately smart for their age)
• お茶の割には美味しい – This is pretty good for tea.
• 犬の割にはいいやつだ – You’re a good “guy” for a dog. (Said by someone who hates dogs)

の割に (and 割に) weakens the statement after it by qualifying it:

• 年の割に若く見える – You look young for your age.
• 若く見える – You look young. 

の割に is basically interchangeable with にしては. (with Nouns)

の割に合わない

の割に合わない
Not worth it

A related phrase is の割に合わない. It is used to express something not being worth it (time, money, etc.)
割に合わない literally means: “isn’t proportional to”., but tends to be used for “worth” statements. 

• このかばんは値段の割に合わない – This bag isn’t worth its price.
• その寺は入場料の割に合わない – That temple isn’t worth its entrance fee.
  
  

A Note about と and に

Both と and に can function to make the word before them an adverb. Typically, only に is used for non speech/quotable words, however there are certain ”と” adverbs, typically onomatopoeia. 
Some words, however may take either. In this cases, to me, と feels like there is some emphasis on a surprise or unexpected result. 

You should let your experience help you determine which you feel is most appropriate for a situation when they come up.