Can you also say 'Ik heb zin in op mijn verjaardag'? I've heard this phrase a lot here.
What's the problem in writing "I look forward for my birthday" rather than using only 'to'..?
Considering "ver" can mean "far", and "verheugen" means "to look forward" ("to look far ahead"), I wonder (Ik vraag me af) whether "HEUGEN" has anything to do with "ogen"... or "to look". So, is "heugen" and "ogen" related? Bedankt, NBL2015
Verheugen is a combination of the prefix ver- and the (uncommon) noun heug. Ver- in this context holds the meaning of change, and heug is an uncommon word for desire / will. Thus, verheugen could literally be interpreted as causing a feeling of desire or will.
Another possibility I can find is that it derives from heugen, which means to remember. This derives from heug as well, though.
(Fun fact: Ge- can turn a verb into a noun, that's why geheugen means memory: ge- + heugen!)
To answer your initial question, oog and heug(en) are not related. They seem to stem from wildly different Proto-Germanic roots.