The front forks have springs inside, one spring in each fork. As standard these are supporting for a rider of about 10st.
As you're rather heavier than the bike was sprung for there are a couple of possibilities. One is simply that you're not used to how a bigger bike reacts to bumps of you've just moved up from a 125 there's a chance that it'll feel very different.
You may find that someone has put some particularly thick fork springs or oil in there, but I'd say the chances of it being over-sprung for 21st aren't very high.
Finally the forks may be soft, and bottoming out, giving you that hard feeling when you run out of travel.
The cable-tie can help check for option 3, fully compressed the forks stop about 10mm or so underneath the bottom yoke / lower fork clamp. If you're using all of that without trying on the road things may bee a little soft
Welcome! If you need any further advice, saying exactly which sv650 you have, and give any history or modifications you know of
Jambo
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