As an infiltrator, we're actually relatively well covered for either option in regards to the staff:
Fight to Win? Jaune Darc has already shown in the preliminary exam that he feels he has something to prove, and wishes to assert his own identity relative to his family name. Beyond that, trying to win a spar isn't exactly weird even without that motivation.
Take a Dive? While Jaeger wasn't there for it, Jaune Darc has already shown concern for Weiss' well-being beforehand, and he might've thought this was a good idea to boost her ego. Might even work, who knows?
Pfft we're not safe on either front here, Ozpin totally already knows, the dude's shifty and insghtful like that. And potentially an old Grimmfiltrator himself, who even knows man?
As another student, there's the more obvious potential issues:
Actually win? Weiss probably flips in one way or another and gets personally ticked at Jaune... which isn't necessarily a bad thing, anger being better then indifference. Also probably gets some degree of respect from the other students for winning.
Might reveal our black goo though.
Actually fight, but lose? Weiss enjoys a win and we conform to current expectations otherwise. Probably get some tips on how to not suck too >_>
Might reveal our black goo though.
Toss the fight convincingly? As above, and Jaeger - who seems pretty chill so far - may-or-may-not rat us out right in front of Weiss
Might reveal our black goo though.
Toss the fight badly? Weiss probably flips over the disrespect, Pyrrha more then likely flips over our being a bad competitor, and we probably lose some respect all around - Jaeger may-or-may-not give a crap while telling us to actually try next time, i'unno.
As before. Simple fact is we're about to get fake-stabbed, fake-frozen, something. We simply don't know how durable the human shell is at the moment, so any combat of any level could potentially reveal our goo. I expect it to require more then a little bruising at least but...
As an infiltrator, the safe option is probably tossing the fight... but we've got 10 more of these coming up and tossing every single one of them is not going to be allowed. We'll be back at the current dilemma eventually anyway.
As a student, the safer option is probably... tossing the fight, because we're more likely to show off unintentionally if we really try to get stuck in, meaning we'll end up shunned/stabbed for being a Grimm, and thus cannot be a student
Better potential gains from fighting. The risks are the same, if somewhat more pronounced.