I have heard others say that very heavy pellets should only be shot out of PCP's, but I don't fully understand why this could cause damage to a springer (as opposed to very low velocity and poor accuracy) or what the threshold is for "too heavy." But, in the old days before PCP's were a big thing, the Beeman Kodiak/H&N Barracuda pellet was already in existence, so I always assumed they were made for high power springers and consider them to be the upper limit for pellet weight.
The HW77/97 powerplant can comforably put out 17fpe in .22 without being overstressed (I have one that shoots shoots smooth as butter at 16.75fpe), so it can handle a pretty heavy pellet. Personally, mine is not pellet picky and shoots almost everything well, but seems to like JSB 15.89 the best (which none of my other .22 Weihrauchs like at all). I'd say your initial selection is a really good start for pellet testing.